{"id":31790,"date":"2023-07-12T12:08:00","date_gmt":"2023-07-12T12:08:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31790"},"modified":"2024-02-05T15:36:46","modified_gmt":"2024-02-05T15:36:46","slug":"empty-set-definition-properties-notation-symbol-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set","title":{"rendered":"Empty Set: Definition, Properties, Notation, Symbol, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-456d7190-d899-440d-8323-ac097d934b93\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set#0-what-is-an-empty-set-in-math>What Is an Empty Set in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set#3-how-to-represent-an-empty-set>How to Represent an Empty Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set#6-difference-between-zero-set-and-empty-set>Difference Between Zero Set and Empty Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set#9-solved-examples-on-empty-set>Solved Examples on Empty Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set#10-practice-problems-on-empty-set>Practice Problems on Empty Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set#11-frequently-asked-questions-on-empty-set>Frequently Asked Questions on Empty Set<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-an-empty-set-in-math\">What Is an Empty Set in Math?<\/h2>\n\n\n\n<p><strong>An empty set is also called a null set or a void set. It is a set that has no elements. An empty set is denoted by <\/strong>$\u2205$ or $\\left\\{ \\right\\}$.<\/p>\n\n\n\n<p>Consider an example. Let\u2019s define set A as the set of perfect squares less than 0. However, we know that a perfect square is always a positive number. It means that the set A has no elements. Thus, it is an empty set. You can think of an empty set as an empty box or an empty container.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-the-sets-of-objects\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_comp_grps_1_pt.png\" alt=\"Compare the Sets of Objects Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare the Sets of Objects Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-out-the-objects-from-a-set\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_count_out_w10_pt.png\" alt=\"Count Out the Objects from a Set Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Out the Objects from a Set Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/make-the-sets-of-objects-equal\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_eql_grps_pt.png\" alt=\"Make the Sets of Objects Equal Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Make the Sets of Objects Equal Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/rearrange-groups-to-make-a-set-bigger\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_rearrange_grps_pt.png\" alt=\"Rearrange Groups to Make a Set Bigger Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Rearrange Groups to Make a Set Bigger Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/set-quarter-hours-on-an-analog-clock\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/time_qrtr_hrs_set_time_words_pt.png\" alt=\"Set Quarter Hours on an Analog Clock Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Set Quarter Hours on an Analog Clock Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/set-the-time-after-an-interval\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/time_set_time_interval_pt.png\" alt=\"Set the Time after an Interval Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Set the Time after an Interval Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/set-the-time\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/time_set_time_pt.png\" alt=\"Set the Time Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Set the Time Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/set-time-in-half-hours\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/time_set_time_half_hours_pt.png\" alt=\"Set Time in Half Hours Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Set Time in Half Hours Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/set-time-in-hours\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/time_set_time_hours_pt.png\" alt=\"Set Time in Hours Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Set Time in Hours Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/set-time-on-an-analog-clock\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/time_5_mins_set_time_ac_pt.png\" alt=\"Set Time on an Analog Clock Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Set Time on an Analog Clock Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-definition-of-empty-set\">Definition of Empty Set<\/h2>\n\n\n\n<p><strong>An empty set can be defined as a set that does not contain any element. It is a set with cardinality 0.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Empty Set Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$P = \\left\\{y: \\text{y is a leap year between 2008 and 2012}\\right\\}$<\/li>\n<\/ul>\n\n\n\n<p>Between 2008 and 2012, there was no leap year.<\/p>\n\n\n\n<p>Therefore, P is a null set.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$Q = \\left\\{x : \\text{x is a prime number and} x \\lt 2\\right\\}$<\/li>\n<\/ul>\n\n\n\n<p>We know that 2 is the only even prime number. However, we have an condition $x \\lt 2$.<\/p>\n\n\n\n<p>Thus, Q is an empty set.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/empty-or-full-worksheet\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/empty-or-full-worksheet.jpeg\" alt=\"Empty or Full Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-fraction-of-a-set-of-objects\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/find-fraction-of-a-set-of-objects.jpeg\" alt=\"Find Fraction of a Set of Objects Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-fraction-of-a-set\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/find-fraction-of-a-set.jpeg\" alt=\"Find Fraction of a Set Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/represent-a-set-of-data\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/represent-a-set-of-data.jpeg\" alt=\"Represent a Set of Data Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/set-time-on-analog-clock\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/set-time-on-analog-clock.jpeg\" alt=\"Set Time on Analog Clock Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/set-time-on-the-clock\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/set-time-on-the-clock.jpeg\" alt=\"Set time on the Clock Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/values-of-sets-of-bills\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/values-of-sets-of-bills.jpeg\" alt=\"Values of Sets of Bills Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/write-the-value-of-a-set-of-coins\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/write-the-value-of-a-set-of-coins.jpeg\" alt=\"Write the Value of a Set of Coins Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-empty-set-symbol\">Empty Set Symbol<\/h2>\n\n\n\n<p>The empty set is denoted by $\u2205$ or $\\left\\{ \\right\\}$.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-represent-an-empty-set\">How to Represent an Empty Set<\/h2>\n\n\n\n<p>As mentioned earlier, we can represent an empty set either with a special symbol \u2205 or with the conventional curly brackets { } with no elements inside. Let\u2019s understand the empty set notation with the help of examples.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$A =$ Set of natural numbers less than $1 = \\left\\{ \\right\\}$.<\/li>\n\n\n\n<li>B is the set of real numbers satisfying $x^{2} + 1 = 0$.<\/li>\n<\/ul>\n\n\n\n<p>The equation doesn&#8217;t have a real solution since -1 is not real.&nbsp;&nbsp;<\/p>\n\n\n\n<p>Thus, $B = \u2205$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\u2205 = \\left\\{x: \\text{x is odd and x is a multiple of 2}\\right\\}$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-properties-of-empty-set\">Properties of Empty Set<\/h2>\n\n\n\n<p>Empty sets are incredibly useful for classifying unusual and odd objects. These empty sets make the calculations simpler. Due to some of their properties, these empty sets are significant.&nbsp;<\/p>\n\n\n\n<p>Let&#8217;s examine these properties in order to better understand the idea of empty sets.<\/p>\n\n\n\n<p><strong>Cardinality<\/strong><\/p>\n\n\n\n<p>The cardinality of a set refers to the total number of elements present in the set. Empty set has no elements. The cardinality of the empty set is zero.&nbsp;<\/p>\n\n\n\n<p>$|\u2205| = 0$<\/p>\n\n\n\n<p><strong>Empty set is a subset of every set.<\/strong><\/p>\n\n\n\n<p>For any set A, the empty set is a subset of A.<\/p>\n\n\n\n<p>&nbsp;$\u2205\\; \u2286$ A for any set A<\/p>\n\n\n\n<p>It does not matter whether a set is finite or infinite. An empty set will always be the subset of the given set.&nbsp;<\/p>\n\n\n\n<p><strong>Subset of an Empty Set<\/strong><\/p>\n\n\n\n<p>The only subset of an empty set is the empty set itself.&nbsp;<\/p>\n\n\n\n<p>If $A \u2286 \\; \u2205 A = \u2205$<\/p>\n\n\n\n<p><strong>Cartesian Product of Empty Set<\/strong><\/p>\n\n\n\n<p>The Cartesian product of any set and the empty set is the empty set.<\/p>\n\n\n\n<p>&nbsp;$A \u2205 = \u2205$<\/p>\n\n\n\n<p><strong>Power Set of Empty Set<\/strong><\/p>\n\n\n\n<p>An empty set or a null set does not contain any element. Thus, the power set of the empty set is the set containing only the empty set.<\/p>\n\n\n\n<p><strong>Union with Empty set<\/strong><\/p>\n\n\n\n<p>The union of A with the empty set is the set A itself. Since an empty set contains no elements at all, its union with any set A produces the same set A.<\/p>\n\n\n\n<p>$A \u22c3 \u2205 = A$<\/p>\n\n\n\n<p><strong>Intersection with Empty Set<\/strong><\/p>\n\n\n\n<p>The intersection of A with the empty set is again the empty set. As the empty set contains no elements, there will be no common element between an empty and a non-empty set.<\/p>\n\n\n\n<p>$A \u22c2 \u2205 = \u2205$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-venn-diagram-of-empty-set\">Venn Diagram of Empty Set<\/h2>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/venn-diagram\"><strong>Venn diagram<\/strong><\/a><strong> is a diagram used to visually represent sets, relationships between sets, and operations on sets.<\/strong><\/p>\n\n\n\n<p>A Venn diagram gives a clear idea about the different relationships between the given sets, such as union, intersection, or complement.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"245\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/representing-empty-set-using-a-venn-diagram.png\" alt=\"Representing empty set using a venn diagram\" class=\"wp-image-31793\" title=\"Representing empty set using a venn diagram\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/representing-empty-set-using-a-venn-diagram.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/representing-empty-set-using-a-venn-diagram-300x119.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Example:<\/strong> Consider two sets.<\/p>\n\n\n\n<p>$A = \\left\\{a, b, c\\right\\}$&nbsp;<\/p>\n\n\n\n<p>$B = \\left\\{d, e, f\\right\\}$&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"356\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/example-of-venn-diagram-of-empty-set.png\" alt=\"Example of venn diagram of empty set\" class=\"wp-image-31794\" title=\"Example of venn diagram of empty set\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/example-of-venn-diagram-of-empty-set.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/example-of-venn-diagram-of-empty-set-300x172.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The Venn diagram shows that there are no common or intersecting elements between the two sets. Therefore we can infer that the intersection between the sets is empty.&nbsp;<\/p>\n\n\n\n<p>Thus, $A \u2229 B = \u2205$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-difference-between-zero-set-and-empty-set\">Difference Between Zero Set and Empty Set<\/h2>\n\n\n\n<figure class=\"wp-block-table wj-custom-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Zero Set<\/strong><\/th><th><strong>Empty Set<\/strong><\/th><\/tr><\/thead><tbody><tr><td>A zero set is a zero set containing 0 as its only element.<\/td><td>The empty set or null set is a set with no elements.<\/td><\/tr><tr><td>Zero set is symbolically represented as $\\left\\{0\\right\\}$.<\/td><td>Empty set is symbolically represented as $\u2205$ or $\\left\\{ \\right\\}$.<\/td><\/tr><tr><td>Cardinality $= 1$<\/td><td>Cardinality $= 0$<\/td><\/tr><tr><td><em>Example:&nbsp;<\/em>A set $A =$ Set of whole numbers less than 1&nbsp;Thus, $A = \\left\\{0\\right\\}$<\/td><td><em>Example:<\/em>A set $B = \\left\\{x: \\text{x is a prime number in between} 7 \\lt x \\lt 11\\right\\}$.Thus, $B = \\left\\{ \\right\\}$ or $\u2205$&nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-facts-about-empty-set\">Facts about Empty Set<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The empty set is also called the null set.<\/li>\n\n\n\n<li>The empty set is unique. It is the only set with no elements in it. There is only one empty set, regardless of the context or the definition of the universal set.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have learned about the empty set, its properties and representation. Let&#8217;s solve some examples and practice problems to understand the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-solved-examples-on-empty-set\">Solved Examples on Empty Set<\/h2>\n\n\n\n<p><strong>1. Determine which of the following sets is empty.<\/strong><\/p>\n\n\n\n<p><strong>a. <\/strong>$\\left\\{x : x + 4 = 7\\right\\}$<\/p>\n\n\n\n<p><strong>b. <\/strong>$\\left\\{x : x^{2} \\;-\\; x = 2 \\right\\}$<\/p>\n\n\n\n<p><strong>c. <\/strong>$\\left\\{x : 7 \\lt x \\lt 8, \\text{x is a natural number.}\\right\\}$<\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>An empty set is a set having no elements.&nbsp;<\/p>\n\n\n\n<p>Let&#8217;s find the elements of each set to determine which set is empty.<\/p>\n\n\n\n<p><strong>a. <\/strong>$\\left\\{x : x + 7 = 7 \\right\\}$<\/p>\n\n\n\n<p>$x = 7 \\;-\\; 7$<\/p>\n\n\n\n<p>$x = 0$<\/p>\n\n\n\n<p>$\\left\\{x: x + 7 = 7\\right\\} = \\left\\{0\\right\\}$&nbsp;<\/p>\n\n\n\n<p>This is a zero set. It is not an empty set.<\/p>\n\n\n\n<p><strong>b. <\/strong>$\\left\\{x : x^{2} \\;-\\; x=2\\right\\}$<\/p>\n\n\n\n<p>$x (x \\;-\\; 1) = 2$&nbsp;<\/p>\n\n\n\n<p>$x = 2$ or $x = \\;-\\; 1$<\/p>\n\n\n\n<p>Thus, it is not an empty set.<\/p>\n\n\n\n<p><strong>c. <\/strong>$\\left\\{x: 7 \\lt x \\lt 8, \\text{x is a whole number.}\\right\\}$<\/p>\n\n\n\n<p>$\\left\\{x : 7 \\lt x \\lt 8, \\text{x is a whole number}\\right\\}$ will be a null set because there is no whole number between numbers 7 and 8.<\/p>\n\n\n\n<p><strong>2. P is the intersection of the set of quadrilaterals with the set of triangles. Is the set P a null set?&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>For a set to be null, the set must be empty, meaning there are no elements in it.&nbsp;<\/p>\n\n\n\n<p>A quadrilateral is a polygon with 4 sides and 4 vertices.<\/p>\n\n\n\n<p>A triangle is a polygon with 3 sides and 3 vertices.<\/p>\n\n\n\n<p>Therefore, the set P is null.<\/p>\n\n\n\n<p><strong>3. Write whether the following statements are true or false.<\/strong><\/p>\n\n\n\n<p><strong>a. An empty set is a subset of every set.<\/strong><\/p>\n\n\n\n<p><strong>b. The set of odd natural numbers divisible by 2 is an empty set.<\/strong><\/p>\n\n\n\n<p><strong>c. The set of odd prime numbers is an empty set.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>a.&nbsp; An empty set is a subset of every set.<\/strong><\/p>\n\n\n\n<p><strong>True.<\/strong><\/p>\n\n\n\n<p>An empty set is a subset of every set.<\/p>\n\n\n\n<p><strong>b. The set of odd natural numbers divisible by 2 is an empty set.<\/strong><\/p>\n\n\n\n<p><strong>True<\/strong><\/p>\n\n\n\n<p>Odd natural numbers are not divisible by 2. There is no natural number that satisfies the condition. Hence, it is an empty set.<\/p>\n\n\n\n<p><strong>c. The set of odd prime numbers is an empty set<\/strong><\/p>\n\n\n\n<p><strong>False<\/strong><\/p>\n\n\n\n<p>The set of odd numbers $= \\left\\{3,\\; 5,\\; 7,\\; 11,\\; 13,\\; 17,\\; 19 \u2026\\right\\}$<\/p>\n\n\n\n<p>The given set has an infinite number of elements, so it is an infinite set.<\/p>\n\n\n\n<p>Therefore, it is not an empty set.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-practice-problems-on-empty-set\">Practice Problems on Empty Set<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Empty Set: Definition, Properties, Notation, Symbol, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the cardinality of an empty set?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">zero<\/div><div class=\"spq_answer_block\" data-value=\"1\">one<\/div><div class=\"spq_answer_block\" data-value=\"2\">two<\/div><div class=\"spq_answer_block\" data-value=\"3\">any<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: zero<br\/>Null set or empty set is a set which does not contain any element. So, the number of elements in a null set is zero.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is the representation of an empty set?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left( \\right)$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\left[ \\right]$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left\\{ \\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\lt\\; \\gt$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\left\\{ \\right\\}$<br\/>An empty set is a set that does not contain any element. It can be represented by $\\left\\{ \\right\\}$ or $\u2205$ symbol.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is an empty set?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Prime numbers up to 10<\/div><div class=\"spq_answer_block\" data-value=\"1\">Even numbers up to 6<\/div><div class=\"spq_answer_block\" data-value=\"2\">Even prime numbers<\/div><div class=\"spq_answer_block\" data-value=\"3\">Factors of 7 that are greater than or 7<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Factors of 7 that are greater than or 7<br\/>A factor of a number is always less than or equal to the number. So, there is no factor of 7, which is greater than 7. It is an empty set.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Find the solution to set $\\left\\{x : \\text{x is a natural number and 2x + 1 = 2}\\right\\}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left\\{1\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\left\\{2\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left\\{12\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\left\\{\\right\\}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\left\\{\\right\\}$<br\/>$2x + 1 = 2$<br>\r\n$2x = 1$<br>\r\n$x = 12$, which is not a natural number.<br>\r\nSo, the set is empty and can be represented by$\\left\\{ \\right\\}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The empty set is also known as the<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">null set<\/div><div class=\"spq_answer_block\" data-value=\"1\">void set<\/div><div class=\"spq_answer_block\" data-value=\"2\">zero set<\/div><div class=\"spq_answer_block\" data-value=\"3\">Both a and b<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Both a and b<br\/>The empty set is a set that contains no elements. It is also known as null set, or void set.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">6<\/span><h3 class=\"sqp_question_text\">Identify the null set symbol.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left\\{0\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\emptyset$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\u2205$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\alpha$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\u2205$<br\/>Null set $= \\left\\{ \\right\\} = \u2205$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Empty Set: Definition, Properties, Notation, Symbol, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Empty Set\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the cardinality of an empty set?\",\n                    \"text\": \"What is the cardinality of an empty set?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Null set or empty set is a set which does not contain any element. 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It can be represented by $$\\\\left\\\\{ \\\\right\\\\}$$ or $$\u2205$$ symbol.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\left\\\\{ \\\\right\\\\}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"An empty set is a set that does not contain any element. It can be represented by $$\\\\left\\\\{ \\\\right\\\\}$$ or $$\u2205$$ symbol.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"An empty set is a set that does not contain any element. It can be represented by $$\\\\left\\\\{ \\\\right\\\\}$$ or $$\u2205$$ symbol.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is an empty set?\",\n                    \"text\": \"Which of the following is an empty set?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A factor of a number is always less than or equal to the number. So, there is no factor of 7, which is greater than 7. It is an empty set.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Prime numbers up to 10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A factor of a number is always less than or equal to the number. So, there is no factor of 7, which is greater than 7. It is an empty set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Even numbers up to 6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A factor of a number is always less than or equal to the number. So, there is no factor of 7, which is greater than 7. It is an empty set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Even prime numbers\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A factor of a number is always less than or equal to the number. So, there is no factor of 7, which is greater than 7. It is an empty set.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Factors of 7 that are greater than or 7\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A factor of a number is always less than or equal to the number. So, there is no factor of 7, which is greater than 7. It is an empty set.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A factor of a number is always less than or equal to the number. So, there is no factor of 7, which is greater than 7. It is an empty set.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the solution to set $$\\\\left\\\\{x : \\\\text{x is a natural number and 2x + 1 = 2}\\\\right\\\\}$$.\",\n                    \"text\": \"Find the solution to set $$\\\\left\\\\{x : \\\\text{x is a natural number and 2x + 1 = 2}\\\\right\\\\}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$2x + 1 = 2$$<br>\r\n$$2x = 1$$<br>\r\n$$x = 12$$, which is not a natural number.<br>\r\nSo, the set is empty and can be represented by$$\\\\left\\\\{ \\\\right\\\\}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{1\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$2x + 1 = 2$$<br>\r\n$$2x = 1$$<br>\r\n$$x = 12$$, which is not a natural number.<br>\r\nSo, the set is empty and can be represented by$$\\\\left\\\\{ \\\\right\\\\}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{2\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$2x + 1 = 2$$<br>\r\n$$2x = 1$$<br>\r\n$$x = 12$$, which is not a natural number.<br>\r\nSo, the set is empty and can be represented by$$\\\\left\\\\{ \\\\right\\\\}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{12\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$2x + 1 = 2$$<br>\r\n$$2x = 1$$<br>\r\n$$x = 12$$, which is not a natural number.<br>\r\nSo, the set is empty and can be represented by$$\\\\left\\\\{ \\\\right\\\\}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\left\\\\{\\\\right\\\\}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$2x + 1 = 2$$<br>\r\n$$2x = 1$$<br>\r\n$$x = 12$$, which is not a natural number.<br>\r\nSo, the set is empty and can be represented by$$\\\\left\\\\{ \\\\right\\\\}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$2x + 1 = 2$$<br>\r\n$$2x = 1$$<br>\r\n$$x = 12$$, which is not a natural number.<br>\r\nSo, the set is empty and can be represented by$$\\\\left\\\\{ \\\\right\\\\}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The empty set is also known as the\",\n                    \"text\": \"The empty set is also known as the\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The empty set is a set that contains no elements. It is also known as null set, or void set.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"null set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The empty set is a set that contains no elements. It is also known as null set, or void set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"void set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The empty set is a set that contains no elements. It is also known as null set, or void set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"zero set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The empty set is a set that contains no elements. It is also known as null set, or void set.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Both a and b\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The empty set is a set that contains no elements. It is also known as null set, or void set.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The empty set is a set that contains no elements. It is also known as null set, or void set.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the null set symbol.\",\n                    \"text\": \"Identify the null set symbol.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Null set $$= \\\\left\\\\{ \\\\right\\\\} = \u2205$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{0\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Null set $$= \\\\left\\\\{ \\\\right\\\\} = \u2205$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\emptyset$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Null set $$= \\\\left\\\\{ \\\\right\\\\} = \u2205$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\alpha$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Null set $$= \\\\left\\\\{ \\\\right\\\\} = \u2205$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\u2205$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Null set $$= \\\\left\\\\{ \\\\right\\\\} = \u2205$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Null set $$= \\\\left\\\\{ \\\\right\\\\} = \u2205$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-frequently-asked-questions-on-empty-set\">Frequently Asked Questions on Empty Set<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-4062b1e8-d133-4521-a3e8-9b531317bbfe\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-4062b1e8-d133-4521-a3e8-9b531317bbfe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4062b1e8-d133-4521-a3e8-9b531317bbfe\"><strong>Why is an empty set called a set?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-4062b1e8-d133-4521-a3e8-9b531317bbfe\">\n\n<p>We know that a set is a collection of well-defined objects. However, if we define a set using conditions that are not satisfied by any real number, the set will have no elements.&nbsp;If you subtract a set from itself, you will get A &#8211; A, which is a set with nothing in it. If the intersection of two sets A and B, since it is possible that A and B have no elements in common (for example, if A is the even integers and B is the odd integers). To define such sets, you need the empty set.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-4062b1e8-d133-4521-a3e8-9b531317bbfe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4062b1e8-d133-4521-a3e8-9b531317bbfe\"><strong>What is the power set of an empty set?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-4062b1e8-d133-4521-a3e8-9b531317bbfe\">\n\n<p>An empty set or a null set does not contain any element. The only subset of the empty set is the empty set itself. Thus, the power set of the empty set is the empty set.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-4062b1e8-d133-4521-a3e8-9b531317bbfe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4062b1e8-d133-4521-a3e8-9b531317bbfe\"><strong>Is an empty set a finite set?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-4062b1e8-d133-4521-a3e8-9b531317bbfe\">\n\n<p>Yes. Empty set has no elements in it. That implies its cardinal number is zero. Therefore, an empty set is considered a finite set.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-4062b1e8-d133-4521-a3e8-9b531317bbfe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4062b1e8-d133-4521-a3e8-9b531317bbfe\"><strong>Is <\/strong>$\\left\\{0\\right\\}$<strong> a null set ?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-4062b1e8-d133-4521-a3e8-9b531317bbfe\">\n\n<p>No, there is one element inside the brackets. So, it is a singleton set, not a null set.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-4062b1e8-d133-4521-a3e8-9b531317bbfe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4062b1e8-d133-4521-a3e8-9b531317bbfe\"><strong>Is <\/strong>$\\left\\{\u2205\\right\\}$<strong> an empty set?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-4062b1e8-d133-4521-a3e8-9b531317bbfe\">\n\n<p>No, $\\left\\{\u2205\\right\\}$ is not an empty set. An empty set is a set that does not contain any elements. The set $\\left\\{\u2205\\right\\}$ contains one element which is $\u2205$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-4062b1e8-d133-4521-a3e8-9b531317bbfe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4062b1e8-d133-4521-a3e8-9b531317bbfe\"><strong>What is a non-empty set?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-4062b1e8-d133-4521-a3e8-9b531317bbfe\">\n\n<p>Any set with at least one element is a non-empty set.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is an Empty Set in Math? An empty set is also called a null set or a void set. It is a set that has no elements. An empty set is denoted by $\u2205$ or $\\left\\{ \\right\\}$. Consider an example. Let\u2019s define set A as the set of perfect squares less than 0. However, &#8230; <a title=\"Empty Set: Definition, Properties, Notation, Symbol, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/empty-set\" aria-label=\"More on Empty Set: Definition, Properties, Notation, Symbol, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-31790","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31790","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=31790"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31790\/revisions"}],"predecessor-version":[{"id":39939,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31790\/revisions\/39939"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31790"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}