{"id":23499,"date":"2023-02-03T08:23:34","date_gmt":"2023-02-03T08:23:34","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=23499"},"modified":"2024-02-05T15:26:42","modified_gmt":"2024-02-05T15:26:42","slug":"what-is-a-set-in-math","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/sets","title":{"rendered":"Set in Math &#8211; Definition, Types, Properties, Examples"},"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-76279ef3-d8ed-4196-af13-8c3705068c3b\" 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\/sets#0-what-is-a-set>What is a Set?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sets#2-elements-of-a-set>Elements of a Set<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sets#6-types-of-sets>Types of Sets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sets#25-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sets#26-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sets#27-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-set\">What is a Set?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We commonly use the terms like \u2018a complete set of novels\u2019 or \u2018a set of cutlery\u2019 in day-to-day life. What do we mean by the term \u2018set\u2019 here? It simply defines a collection of objects or things of the same type. Sets in math are also defined in the similar context.<\/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\/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><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 eplus-wrapper\" id=\"1-set-definition\">Set Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In mathematics, a set is defined as a collection of distinct, well-defined objects forming a group. There can be any number of items, be it a collection of whole numbers, months of a year, types of birds, and so on. Each item in the set is known as an element of the set. We use curly brackets while writing a set.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Consider an example of a set.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} = \\left\\{1, 3, 5, 7, 9\\right\\}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">It has five elements. It is a set of odd numbers less from 1 to 10.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">What do we mean by \u2018well-defined\u2019 objects?<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Consider an example. A collection of odd natural numbers less than 20 is defined, but a collection of brave students in a class is not defined.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can represent a collection of odd natural numbers less than 20 in the form of a set as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{B} = \\left\\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19\\right\\}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The number of elements in the set are denoted by n(A) where A is a set.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $\\text{A} = \\left\\{1, 4, 9, 16, 25, 36, 49, 64, 81, 100\\right\\}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$n(A) = 10$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The other word used for the number of elements in the set is called its cardinality.&nbsp;<\/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\/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><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 eplus-wrapper\" id=\"2-elements-of-a-set\">Elements of a Set<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Elements or members are the terms or items present in a set. They are enclosed in curly brackets and separated by commas. To represent that an element is contained in a set, we use the symbol \u201c$\\in$.\u201d It is read as \u2018belongs to.\u2019<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Suppose we have a set of even natural numbers less than 10.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} = \\left\\{2, 4, 6, 8\\right\\}$ .<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $2 \\in A$ but $3 \\notin A$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-representation-of-sets\">Representation of Sets<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We represent the sets in different ways. The only difference is in the way in which the elements are listed. The different forms of representing sets are discussed below.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-roster-form\">Roster Form<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The most familiar and easy form used to represent sets is the roster form, in which the elements are enclosed in curly brackets and are separated by commas such as $\\text{B} = \\left\\{1, 4, 9, 16, 25\\right\\}$, which is the collection of the square of consecutive numbers less than 30. The order of the elements does not matter and there can be an infinite number of elements in a set, which we define using a series of dots at the end of the last element. There are two types of sets in Roster Form:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Finite Roster Notation of Sets in which there are elements that can be counted, such as $\\text{A} = \\left\\{5, 10, 15, 20, 25\\right\\}$ (The multiples of 5 less than 30.)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Infinite Roster Notation of Sets in which the elements can not be counted, such as $\\text{B} = \\left\\{4, 8, 12, 16 &#8230;\\right\\}$ (The multiples of 4)<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-set-builder-form\">Set Builder Form<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The set builder notation has a particular rule that describes the common feature of all the elements of a set. It uses a vertical bar in its representation along with a text describing the character of the elements, such as $\\text{A} = \\left\\{ \\text{x}\\; |\\; \\text{x} \\; \\text{is a prime number}, x \\le 20\\right\\}$. According to the statement, all the elements of the set are prime numbers less than or equal to 20. We use \u201c:\u201d place of the \u201c|\u201d sometimes.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-types-of-sets\">Types of Sets<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s discuss different types of sets.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-singleton-sets\">Singleton Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">When a set has only one element, it is known as a singleton set.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Set $\\text{A} = \\left\\{ \\text{x}\\; |\\; \\text{x}\\; \\text{is a whole number between}\\;12\\; \\text{and}\\;14\\right\\} = \\left\\{13\\right\\}$.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"8-null-or-empty-sets\">Null or Empty Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">When a set does not contain any element, it is known as a null or an empty set. It is denoted by the symbol \u201c$\\Phi$\u201d and it is read as \u201cphi.\u201d&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Set $\\text{B} = =$ Integers between 1 and $2 = \\Phi$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"9-equal-sets\">Equal Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Two sets are said to be equal if they have the same elements in them. Suppose there are two sets $\\text{A} = \\left\\{1, 4, 5\\right\\}$ and $\\text{B} = \\left\\{1, 4, 5\\right\\}$. Here, $\\text{A} = \\text{B}$ because each element is the same.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"10-unequal-sets\">Unequal Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Two sets are said to be unequal if they have at least one different element. Suppose we have two sets $\\text{A} = \\left\\{1, 2, 5\\right\\}$ and $\\text{B} = \\left\\{1, 2, 4\\right\\}$. Here, $\\text{A} \\neq \\text{B}$ as $5 \\in \\text{A}$ but $5 \\notin \\text{B}$.&nbsp;&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"11-equivalent-sets\">Equivalent Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Equivalent sets are the two sets that have the same number of elements, even if the elements are different. Suppose we have two sets $\\text{A} = \\left\\{10, 11, 12, 13\\right\\}$ and $\\text{B} = \\left\\{January, February, March, April\\right\\}$. Since $n(A) = n(B)$, A and B are equivalent sets.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"12-overlapping-sets\">Overlapping Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">If at least one element from set A is present in set B, then the sets are said to be overlapping. Example: $\\text{A} = \\left\\{2, 3, 6\\right\\} \\text{B} = \\left\\{6, 8, 12\\right\\}$. 6 is present in set A and set B. So, A and B are overlapping sets.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"13-subset-and-superset\">Subset and Superset<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">If every element in set A is also present in set B, then set A is known as the subset of set B, which is denoted by $\\text{A} \\subseteq \\text{B}$ and B is known as the superset of set A, which is denoted by $\\text{B} \\supseteq \\text{A}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $\\text{A} = \\left\\{1, 4, 7, 10, 12\\right\\}\\; \\text{B} = \\left\\{1, 4, 6, 7, 8, 10, 11, 12, 13\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} \\subseteq \\text{B}$, since all the elements of A are present in B.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Also, set B is the superset of set A.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"14-universal-set\">Universal Set<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The collection of all the elements in regard to a particular subject is known as a universal set which is denoted by the letter \u201cU.\u201d Suppose we have a set U as the set of all the natural numbers. So, the set of even numbers, set of odd numbers, set of prime numbers is a subset of the universal set.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"15-disjoint-sets\">Disjoint Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Two sets are known as disjoint sets if they have no common elements in both sets. Consider two sets &#8211; $\\text{A} = \\left\\{5, 6, 7\\right\\}$ and $\\text{B} = \\left\\{2, 3, 4\\right\\}$. Here, set A and set B are disjoint sets as they have no elements in common.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"16-power-sets\">Power Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The set of all subsets that a set could contain is known as the power set. Suppose we have a set $\\text{A} = \\left\\{2, 3\\right\\}$. Power set of A is $= \\left\\{\\left\\{\\varnothing\\right\\}, \\left\\{2\\right\\}, \\left\\{3\\right\\}, \\left\\{2,3\\right\\}\\right\\}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If n is the number of elements in a set, then the number of subsets $=2^{n}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"17-visual-representation-of-sets-using-venn-diagram\">Visual Representation of Sets Using Venn Diagram<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The pictorial representation of sets represented as circles is known as the Venn diagram. The elements of the sets are inside the circles. The rectangle that encloses the circles represents the universal set. The Venn diagram represents how the sets are related to each other.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"543\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/venn-diagram-displaying-elements-of-two-sets.png\" alt=\"Venn diagram displaying elements of two sets\" class=\"wp-image-36863\" title=\"Venn diagram displaying elements of two sets\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/venn-diagram-displaying-elements-of-two-sets.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/venn-diagram-displaying-elements-of-two-sets-300x263.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"18-operations-on-sets\">Operations on Sets<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are some operations on sets given below:&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"19-union-of-sets\">Union of Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">B. Suppose we have two sets $\\text{A} = \\left\\{1, 2, 3\\right\\}$ and $\\text{B} = \\left\\{3, 4, 5\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A}\\; \\text{U}\\; \\text{B} = \\left\\{1, 2, 3, 4, 5\\right\\}$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"20-intersection-of-sets\">Intersection of Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The intersection of sets is denoted by $\\text{A} \\cap \\text{B}$ has the elements which are common in both set A and set B. Suppose we have two sets $\\text{A} = \\left\\{1, 3\\right\\}$ and $\\text{B} = \\left\\{3, 4\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} \\cap \\text{B} = {3}$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"21-difference-of-sets\">Difference of Sets<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">We denote the set difference by $\\text{A} \u2013 \\text{B}$, which has the elements in set A that are not present in set B. Suppose we have two sets, i.e.,&nbsp; $\\text{A} = \\left\\{3, 4, 5\\right\\}$ and $\\text{B} = \\left\\{5, 6, 7\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} \\;\u2013\\; \\text{B} = \\left\\{3, 4\\right\\}$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"22-complement-of-a-set\">Complement of a Set<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The complement of a set A is denoted by A&#8217;, which is the set of all elements in the universal set that are not present in set A. A&#8217; can also be represented as $\\text{U} \\;\u2013\\; \\text{A}$, i.e., the difference in the elements of the universal set and set A.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Suppose $\\text{U} =$ Set of Natural Numbers and $\\text{A} =$ Set of Prime Numbers<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $\\text{U} \\;\u2013\\; \\text{A} =$ Set of all Non-prime Numbers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"581\" height=\"1024\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/venn-diagrams-of-operations-on-sets.png\" alt=\"Venn diagrams of operations on sets\" class=\"wp-image-36865\" title=\"Venn diagrams of operations on sets\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/venn-diagrams-of-operations-on-sets.png 581w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/venn-diagrams-of-operations-on-sets-170x300.png 170w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"23-sets-formulas\">Sets Formulas<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are some set formulas that we can use to find the number of elements.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For sets A and B,<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$n(A\\; U\\; B) = n(A) + n(B) &#8211; n(A \\cap B)$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$n(A \u2212 B) = n(A U B) \u2212 n(B)$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$n(A \u2212 B) = n(A) \u2212 n(A \\cap B)$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"24-properties-of-sets\">Properties of Sets<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Here are the properties of sets:<\/p>\n\n\n\n<figure class=\"wp-block-table wj-custom-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Set Property<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Representation<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Commutative Property<\/td><td class=\"has-text-align-center\" data-align=\"center\">A \u222a B = B \u222a A<br>A \u22c2 B = B \u22c2 A<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Associative Property<\/td><td class=\"has-text-align-center\" data-align=\"center\">A \u222a (B \u222a C)&nbsp; = (A \u222a B) \u222a C<br>A \u22c2 (B \u22c2 C)&nbsp; = (A \u22c2 B) \u22c2 C<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Distributive Property&nbsp;<\/td><td class=\"has-text-align-center\" data-align=\"center\">A \u222a (B \u22c2 C)&nbsp; = (A \u222a B) \u22c2 (A \u222a C)<br>A \u22c2 (B \u222a C)&nbsp; = (A \u22c2 B) \u222a (A \u22c2 C)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Identity Property<\/td><td class=\"has-text-align-center\" data-align=\"center\">A \u222a \u2205 = A<br>A \u22c2 U = A<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Complement Property<\/td><td class=\"has-text-align-center\" data-align=\"center\">A \u222a A\u2019 = U<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Idempotent Property<\/td><td class=\"has-text-align-center\" data-align=\"center\">A \u222a A = A<br>A \u22c2 A = A<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\" rowspan=\"2\">Properties of \u2205 and U<\/td><td class=\"has-text-align-center\" data-align=\"center\">A \u222a \u2205 = A<br>A \u22c2 \u2205 = \u2205<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">A \u222a U = U<br>A \u22c2 U = A<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"25-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. How many elements are there in the set <\/strong>$\\text{A} = \\left\\{ \\text{x}\\; : \\text{x}\\; \\text{is a perfect square less than 30}\\right\\}$<strong><strong> ?<\/strong><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>$\\text{A} = \\left\\{1, 4, 9, 16, 25\\right\\}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$n(A) = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. <strong>Arrange the set <\/strong><\/strong>$A = \\left\\{ y : y^{2} = 36 ; y\\; \\text{is an integer}\\right\\}$<strong><strong> in roster form.<\/strong><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> $y^{2} = 36 \\Rightarrow y^{2} \u2212 36 = 0 \\Rightarrow y = \\pm 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} = { \u2013\\; 6, 6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Write the set <\/strong>$\\text{B} = \\left\\{1, 2, 5, 10, 17\\right\\}$<strong> in set builder form.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> $0^{2} + 1 = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1^{2} + 1 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2^{2} + 1 = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3^{2} + 1 = 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$4^{2} + 1 = 17$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, in roaster form $\\text{B} = \\left\\{y : y^{2} + 1, y \\lt 5\\right\\}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. If A is a set of prime numbers and B is a set of even numbers. What will be <\/strong>$\\text{A} \\cap \\text{B}$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>Only 2 is the number, which is a prime number as well as an even number. So,&nbsp; $\\text{A} \\cap \\text{B} = {2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Draw a Venn diagram for the sets <\/strong>$\\text{A} = \\left\\{1, 3, 6, 9, 11, 15, 17\\right\\}$<strong> and <\/strong>$\\text{B} = \\left\\{2, 4, 9, 11, 13, 17\\right\\}$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"433\" height=\"289\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sets-in-venn-diagram-example.png\" alt=\"Sets in Venn diagram example\" class=\"wp-image-36866\" title=\"Sets in Venn diagram example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sets-in-venn-diagram-example.png 433w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sets-in-venn-diagram-example-300x200.png 300w\" sizes=\"auto, (max-width: 433px) 100vw, 433px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"26-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">What is a Set in Math<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following sets denotes $\\left\\{\\right\\}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Finite Set<\/div><div class=\"spq_answer_block\" data-value=\"1\">Singleton set<\/div><div class=\"spq_answer_block\" data-value=\"2\">Null Set<\/div><div class=\"spq_answer_block\" data-value=\"3\">Infinite Set<\/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: Null Set<br\/>There is no element in $\\left\\{\\right\\}$. So, it is a null set.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If $\\text{A} = \\left\\{\\;\u2013\\; 1, 0, 2, 3, 5, 7\\right\\}$ and $\\text{B} = \\left\\{0, 1, 2, 3, 5, 6\\right\\}$, then what is $\\text{A}\\; \\text{U}\\; \\text{B}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left\\{ 0, 1, 2, 3, 5, 6, 7\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\left\\{ 0, 2, 3, 5\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left\\{\\; \u2013\\; 1, 1, 7\\right\\}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\left\\{\\; \u2013\\; 1, 0, 1, 2, 3, 5, 6, 7\\right\\}$<\/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: $\\left\\{\\; \u2013\\; 1, 0, 1, 2, 3, 5, 6, 7\\right\\}$<br\/>$\\text{A}\\; \\text{U}\\; \\text{B} = \\left\\{\\; \u2013\\; 1, 0, 1, 2, 3, 5, 6, 7\\right\\}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If $\\text{P} = \\left\\{ \\;\u2013\\; 10, \\;\u2013\\; 7, \\;\u2013\\; 4, \\;\u2013\\; 3, \\;\u2013\\; 2, \\;\u2013\\; 1\\right\\}$ and $\\text{Q} = \\left\\{ \\;\u2013\\; 9, \\;\u2013\\; 8, \\;\u2013\\; 7, \\;\u2013\\; 6, \\;\u2013\\; 4, \\;\u2013\\; 2\\right\\}$ then __ denotes $\\left\\{ \\;\u2013\\; 10, \\;\u2013\\; 3, \\;\u2013\\; 1\\right\\}$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\text{P} \\;\u2013\\; \\text{Q}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\text{P} \\cap \\text{Q}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\text{P} \\cup \\text{Q}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$P\u2019$<\/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: $\\text{P} \\;\u2013\\; \\text{Q}$<br\/>The elements in $\\left\\{ \\;\u2013\\; 10, \\;\u2013\\; 3, \\;\u2013\\; 1\\right\\}$ are elements that are in Set P but not in Set Q.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">How many subsets will be there if $n(A) = 3$ where A is a set?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">6<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">10<\/div><div class=\"spq_answer_block\" data-value=\"3\">12<\/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: 8<br\/>Number of subsets $= 2^{n} = 2^{3} = 8$<\/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\">If $n(A)$ = $16,n (B) = 18$ and $n(A \\cup B) = 7$, then what is the value of $n(A \\cup B)$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">41<\/div><div class=\"spq_answer_block\" data-value=\"1\">9<\/div><div class=\"spq_answer_block\" data-value=\"2\">15<\/div><div class=\"spq_answer_block\" data-value=\"3\">27<\/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: 27<br\/>$n(A \\cup B) = n(A) + n(B) \\;-\\; n(AB) = 16 + 18 \\;-\\; 7 = 27$<\/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\": \"What is a Set in Math\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"What is a Set in Math\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following sets denotes $$\\\\left\\\\{\\\\right\\\\}$$?\",\n                    \"text\": \"Which of the following sets denotes $$\\\\left\\\\{\\\\right\\\\}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"There is no element in $$\\\\left\\\\{\\\\right\\\\}$$. So, it is a null set.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Finite Set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There is no element in $$\\\\left\\\\{\\\\right\\\\}$$. So, it is a null set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Singleton set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There is no element in $$\\\\left\\\\{\\\\right\\\\}$$. So, it is a null set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Infinite Set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There is no element in $$\\\\left\\\\{\\\\right\\\\}$$. So, it is a null set.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Null Set\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"There is no element in $$\\\\left\\\\{\\\\right\\\\}$$. So, it is a null set.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"There is no element in $$\\\\left\\\\{\\\\right\\\\}$$. So, it is a null set.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$\\\\text{A} = \\\\left\\\\{\\\\;\u2013\\\\; 1, 0, 2, 3, 5, 7\\\\right\\\\}$$ and $$\\\\text{B} = \\\\left\\\\{0, 1, 2, 3, 5, 6\\\\right\\\\}$$, then what is $$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B}$$?\",\n                    \"text\": \"If $$\\\\text{A} = \\\\left\\\\{\\\\;\u2013\\\\; 1, 0, 2, 3, 5, 7\\\\right\\\\}$$ and $$\\\\text{B} = \\\\left\\\\{0, 1, 2, 3, 5, 6\\\\right\\\\}$$, then what is $$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B} = \\\\left\\\\{\\\\; \u2013\\\\; 1, 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{ 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B} = \\\\left\\\\{\\\\; \u2013\\\\; 1, 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{ 0, 2, 3, 5\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B} = \\\\left\\\\{\\\\; \u2013\\\\; 1, 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left\\\\{\\\\; \u2013\\\\; 1, 1, 7\\\\right\\\\}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B} = \\\\left\\\\{\\\\; \u2013\\\\; 1, 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\left\\\\{\\\\; \u2013\\\\; 1, 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B} = \\\\left\\\\{\\\\; \u2013\\\\; 1, 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\text{A}\\\\; \\\\text{U}\\\\; \\\\text{B} = \\\\left\\\\{\\\\; \u2013\\\\; 1, 0, 1, 2, 3, 5, 6, 7\\\\right\\\\}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$\\\\text{P} = \\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 7, \\\\;\u2013\\\\; 4, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 2, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ and $$\\\\text{Q} = \\\\left\\\\{ \\\\;\u2013\\\\; 9, \\\\;\u2013\\\\; 8, \\\\;\u2013\\\\; 7, \\\\;\u2013\\\\; 6, \\\\;\u2013\\\\; 4, \\\\;\u2013\\\\; 2\\\\right\\\\}$$ then __ denotes $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$\",\n                    \"text\": \"If $$\\\\text{P} = \\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 7, \\\\;\u2013\\\\; 4, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 2, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ and $$\\\\text{Q} = \\\\left\\\\{ \\\\;\u2013\\\\; 9, \\\\;\u2013\\\\; 8, \\\\;\u2013\\\\; 7, \\\\;\u2013\\\\; 6, \\\\;\u2013\\\\; 4, \\\\;\u2013\\\\; 2\\\\right\\\\}$$ then __ denotes $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The elements in $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ are elements that are in Set P but not in Set Q.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{P} \\\\cap \\\\text{Q}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The elements in $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ are elements that are in Set P but not in Set Q.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{P} \\\\cup \\\\text{Q}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The elements in $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ are elements that are in Set P but not in Set Q.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$P\u2019$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The elements in $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ are elements that are in Set P but not in Set Q.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\text{P} \\\\;\u2013\\\\; \\\\text{Q}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The elements in $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ are elements that are in Set P but not in Set Q.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The elements in $$\\\\left\\\\{ \\\\;\u2013\\\\; 10, \\\\;\u2013\\\\; 3, \\\\;\u2013\\\\; 1\\\\right\\\\}$$ are elements that are in Set P but not in Set Q.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How many subsets will be there if $$n(A) = 3$$ where A is a set?\",\n                    \"text\": \"How many subsets will be there if $$n(A) = 3$$ where A is a set?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Number of subsets $$= 2^{n} = 2^{3} = 8$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Number of subsets $$= 2^{n} = 2^{3} = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Number of subsets $$= 2^{n} = 2^{3} = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Number of subsets $$= 2^{n} = 2^{3} = 8$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Number of subsets $$= 2^{n} = 2^{3} = 8$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Number of subsets $$= 2^{n} = 2^{3} = 8$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$n(A)$$ = $$16,n (B) = 18$$ and $$n(A \\\\cup B) = 7$$, then what is the value of $$n(A \\\\cup B)$$?\",\n                    \"text\": \"If $$n(A)$$ = $$16,n (B) = 18$$ and $$n(A \\\\cup B) = 7$$, then what is the value of $$n(A \\\\cup B)$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$n(A \\\\cup B) = n(A) + n(B) \\\\;-\\\\; n(AB) = 16 + 18 \\\\;-\\\\; 7 = 27$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"41\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$n(A \\\\cup B) = n(A) + n(B) \\\\;-\\\\; n(AB) = 16 + 18 \\\\;-\\\\; 7 = 27$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$n(A \\\\cup B) = n(A) + n(B) \\\\;-\\\\; n(AB) = 16 + 18 \\\\;-\\\\; 7 = 27$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$n(A \\\\cup B) = n(A) + n(B) \\\\;-\\\\; n(AB) = 16 + 18 \\\\;-\\\\; 7 = 27$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"27\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$n(A \\\\cup B) = n(A) + n(B) \\\\;-\\\\; n(AB) = 16 + 18 \\\\;-\\\\; 7 = 27$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$n(A \\\\cup B) = n(A) + n(B) \\\\;-\\\\; n(AB) = 16 + 18 \\\\;-\\\\; 7 = 27$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"27-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\" 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-0-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\"><strong>What are sets formula if sets are disjoint?<\/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-0-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\">\n\n<p class=\"eplus-wrapper\">For disjoint sets A and B;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$n(A U B) = n(A) + n(B)$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$A \\cap B = \\varnothing$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$n(A \u2212 B) = n(A)$<\/li>\n<\/ul>\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-1-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\"><strong>Is {0} 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-1-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\">\n\n<p class=\"eplus-wrapper\">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-2-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\"><strong>What is a Cartesian Product in sets?<\/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-2-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\">\n\n<p class=\"eplus-wrapper\">Cartesian Product of Set A and B is defined as an ordered pair $(x, y)$ where $x \\in A$ and $y \\in B$.<\/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-3-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\"><strong>How is set theory applicable in daily lives?<\/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-3-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\">\n\n<p class=\"eplus-wrapper\">In real life, sets are used in bookshelves while arranging the books according to alphabetic order or genre; closets where dresses, tops, jeans are kept as a set, etc.<\/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-4-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\"><strong>Does the union of two sets include the intersection of the sets?<\/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-4-96865e28-2edc-4dbb-9dc8-c7f74d8ca87b\">\n\n<p class=\"eplus-wrapper\">Yes, the union of two sets includes the intersection of the sets. Union of set A and B includes the elements either in set A or in set B or in both set A and B.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is a Set? We commonly use the terms like \u2018a complete set of novels\u2019 or \u2018a set of cutlery\u2019 in day-to-day life. What do we mean by the term \u2018set\u2019 here? It simply defines a collection of objects or things of the same type. Sets in math are also defined in the similar context. &#8230; <a title=\"Set in Math &#8211; Definition, Types, Properties, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/sets\" aria-label=\"More on Set in Math &#8211; Definition, Types, Properties, Examples\">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-23499","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\/23499","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=23499"}],"version-history":[{"count":93,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23499\/revisions"}],"predecessor-version":[{"id":39918,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/23499\/revisions\/39918"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=23499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=23499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=23499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}