{"id":34102,"date":"2023-09-12T13:25:53","date_gmt":"2023-09-12T13:25:53","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34102"},"modified":"2023-09-17T13:41:01","modified_gmt":"2023-09-17T13:41:01","slug":"disjoint-sets-definition-symbol-facts-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/disjoint-sets","title":{"rendered":"Disjoint Sets: Definition, Symbol, Facts, 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-8d296137-93f9-4784-a168-8f01321e3cf3\" 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\/disjoint-sets#0-what-are-disjoint-sets>What Are Disjoint Sets?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/disjoint-sets#2-disjoint-sets-venn-diagram>Disjoint Sets Venn Diagram<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/disjoint-sets#4-how-to-find-if-two-sets-are-disjoint-sets>How to Find if Two Sets Are Disjoint Sets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/disjoint-sets#7-solved-examples-on-disjoint-sets>Solved Examples on Disjoint Sets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/disjoint-sets#8-practice-problems-on-disjoint-sets>Practice Problems on Disjoint Sets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/disjoint-sets#9-frequently-asked-questions-on-disjoint-sets>Frequently Asked Questions on Disjoint Sets<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-disjoint-sets\">What Are Disjoint Sets?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Disjoint sets are two sets that have no common elements. In other words, their intersection is the empty set.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">What does disjoint mean? The term disjoint simply means \u201cnot connected.\u201d So, disjoint sets are the non-intersecting sets; they have no elements in common.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 1: <\/strong>Consider two sets:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = {2, 3, 4}\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B = {5, 6, 7}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There is no element common in both sets. A \u2229 B is the empty set. Thus, we can say that the sets are disjoint.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"447\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram-of-mutually-disjoint-set-A-and-set-b.png\" alt=\"Venn diagram of mutually disjoint Set A and Set B\" class=\"wp-image-34108\" title=\"Venn diagram of mutually disjoint Set A and Set B\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram-of-mutually-disjoint-set-A-and-set-b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram-of-mutually-disjoint-set-A-and-set-b-300x216.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 2: <\/strong>P = {0, 1, 2} , Q = {1, 2, 3}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P and Q are not disjoint since<strong> <\/strong>P \u2229 Q = {1, 2} $\\neq$ \u2205<\/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\" id=\"1-disjoint-sets-definition\">Disjoint Sets Definition<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In set theory, two sets are called disjoint if the intersection is the empty set or null set.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A and B are disjoint sets if and only if A \u2229 B = \u2205.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A collection of two or more sets is said to be disjoint if the intersection of every pair in the collection 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\/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\" id=\"2-disjoint-sets-venn-diagram\">Disjoint Sets Venn Diagram<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Disjoint sets can easily be determined using a Venn diagram. Venn diagram shows how sets are related to each other, and it also helps to understand different operations on the sets.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"500\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram-of-disjoint-sets.png\" alt=\"Venn diagram of disjoint sets\" class=\"wp-image-34109\" title=\"Venn diagram of disjoint sets\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram-of-disjoint-sets.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram-of-disjoint-sets-300x242.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-pairwise-disjoint-sets\">Pairwise Disjoint Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A collection or family of sets <strong>S<\/strong> is said to be pairwise disjoint if the intersection of every pair of sets in the collection is the empty set. It is also called mutually disjoint sets.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud835\udc4b \u2229 \ud835\udc4c = \u2205 for X, Y \u2208 <strong>S <\/strong>and<strong> <\/strong>X \u2260 Y<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-how-to-find-if-two-sets-are-disjoint-sets\">How to Find if Two Sets Are Disjoint Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">To assess if two sets are disjoint, we must find the intersection of the two sets. If the intersection result is empty, then the sets are disjoint.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M = {0, 1, 2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N = {2, 3, 4}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O = {4, 5, 6}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, by intersecting each pair of sets, we gain<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M \u2229 N = {0, 1, 2} \u2229 {2, 3, 4} = {2};<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N \u2229 O = {2, 3, 4} \u2229 {4, 5, 6} = {4};<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">M \u2229 O = {0, 1, 2} \u2229 {4, 5, 6} = \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As a result, the sets M and O are disjoint sets.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Note:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, the joint intersection of three sets is the null set (M \u2229 N \u2229 O=\u2205), but the three sets are not disjoint. It is because every pair within the group is not disjoint.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-facts-about-disjoint-sets\">Facts about Disjoint Sets<\/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-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Partition of the larger sets can be done through disjoint set theory. It helps to separate larger sets into non-overlapping or smaller subsets.<\/li>\n\n\n\n<li>The empty set is disjoint with itself.<\/li>\n\n\n\n<li>The empty set is the only set that is disjoint with itself.<\/li>\n\n\n\n<li>The empty set is disjoint from every set.<\/li>\n\n\n\n<li>A group of sets may have a null intersection without being disjoint. For example, the three sets {a, b}, {b, c}, and {a, c} have a null intersection (the joint intersection of three sets is empty), but they are not disjoint. No two sets in this group are disjoint.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we learned about disjoint sets, important definitions, and how to find disjoint sets with examples. Let\u2019s recall these concepts and solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved-examples-on-disjoint-sets\">Solved Examples on Disjoint Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Find out if the given set <\/strong><strong>P = {2, 4}<\/strong><strong> and <\/strong><strong>Q = {4, 5}<\/strong><strong> are disjoint.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P = {2, 4} and Q = {4, 5}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P \u2229 Q = {2,4} \u2229 {4, 5}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P \u2229 Q = {4}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P \u2229 Q \u2260 \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the intersection of P and Q is not empty, the given two sets are not disjoint sets.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. <\/strong><strong>A = {a, b}, B = {2, 3)<\/strong><strong> and <\/strong><strong>C = {c, d}<\/strong><strong>. Find the disjoint sets.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution: <\/strong>Given:&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = {a, b}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B = {2, 3}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C = {c, d}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine the disjoint sets, we will calculate the intersections of the given set:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u2229 B = {a, b} \u2229 {2, 3} = \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B \u2229 C = {2, 3} \u2229 {c, d} = \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u2229 C = {a, b} \u2229 {c, d}= \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, as per the intersection analysis, all three sets show a null intersection. Therefore, sets A, B and C are disjoint with each other.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. A = {Earth, Jupiter}, B = {Pluto}, C = {Mercury, Venus}. Prove that A, B, and C are disjoint sets.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution: <\/strong>Given:&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u2229 B ={Earth, Jupiter}\u2229{Pluto} = \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u2229 C ={Earth, Jupiter}\u2229{Mercury, Venus} = \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B \u2229 C ={Pluto}\u2229{Mercury, Venus} = \u2205<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each pair is disjoint. Thus, the sets A, B, C are disjoint sets.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-disjoint-sets\">Practice Problems on Disjoint Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Disjoint Sets: Definition, Symbol, Facts, 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\">A = {0, 2, 4, 6, \u2026} , B = {1, 3, 5, 7, \u2026}<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A and B are disjoint.<\/div><div class=\"spq_answer_block\" data-value=\"1\">A and B are equal.<\/div><div class=\"spq_answer_block\" data-value=\"2\">A and B<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above is correct.<\/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: A and B are disjoint.<br\/>The set A is the set of even numbers. The set B is the set of odd numbers.<br>\r\nThey have no element in common. They are disjoint.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the intersection of disjoint sets?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{0}<\/div><div class=\"spq_answer_block\" data-value=\"1\">\u2205<\/div><div class=\"spq_answer_block\" data-value=\"2\">{1}<\/div><div class=\"spq_answer_block\" data-value=\"3\">0<\/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\/>The intersection of disjoint sets is the null set \u2205.<\/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\">A\/An _____ is disjoint with every set.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">empty set<\/div><div class=\"spq_answer_block\" data-value=\"1\">{0}<\/div><div class=\"spq_answer_block\" data-value=\"2\">universal set<\/div><div class=\"spq_answer_block\" data-value=\"3\">singleton 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: empty set<br\/>An empty set is disjoint with every set.<\/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\">Sets P and Q are disjoint sets if<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">P \u2229 Q \u2260 \u2205<\/div><div class=\"spq_answer_block\" data-value=\"1\">P \u2229 Q \u2260 \u2205<\/div><div class=\"spq_answer_block\" data-value=\"2\">P$\\cup$Q = \u2205<\/div><div class=\"spq_answer_block\" data-value=\"3\">P$\\cup$Q \u2260 \u2205<\/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: P \u2229 Q \u2260 \u2205<br\/>Sets P and Q are disjoint sets if the intersection of the two sets is a null set, P \u2229 Q = \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\": \"Disjoint Sets: Definition, Symbol, Facts, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Disjoint Sets\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A = {0, 2, 4, 6, \u2026} , B = {1, 3, 5, 7, \u2026}\",\n                    \"text\": \"A = {0, 2, 4, 6, \u2026} , B = {1, 3, 5, 7, \u2026}\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The set A is the set of even numbers. The set B is the set of odd numbers.<br>\r\nThey have no element in common. They are disjoint.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A and B are equal.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The set A is the set of even numbers. The set B is the set of odd numbers.<br>\r\nThey have no element in common. They are disjoint.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A and B\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The set A is the set of even numbers. The set B is the set of odd numbers.<br>\r\nThey have no element in common. They are disjoint.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above is correct.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The set A is the set of even numbers. The set B is the set of odd numbers.<br>\r\nThey have no element in common. They are disjoint.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"A and B are disjoint.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The set A is the set of even numbers. The set B is the set of odd numbers.<br>\r\nThey have no element in common. They are disjoint.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The set A is the set of even numbers. The set B is the set of odd numbers.<br>\r\nThey have no element in common. They are disjoint.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the intersection of disjoint sets?\",\n                    \"text\": \"What is the intersection of disjoint sets?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The intersection of disjoint sets is the null set \u2205.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{0}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The intersection of disjoint sets is the null set \u2205.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{1}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The intersection of disjoint sets is the null set \u2205.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The intersection of disjoint sets is the null set \u2205.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"\u2205\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The intersection of disjoint sets is the null set \u2205.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The intersection of disjoint sets is the null set \u2205.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A\/An _____ is disjoint with every set.\",\n                    \"text\": \"A\/An _____ is disjoint with every set.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"An empty set is disjoint with every set.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{0}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An empty set is disjoint with every set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"universal set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An empty set is disjoint with every set.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"singleton set\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An empty set is disjoint with every set.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"empty set\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"An empty set is disjoint with every set.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"An empty set is disjoint with every set.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Sets P and Q are disjoint sets if\",\n                    \"text\": \"Sets P and Q are disjoint sets if\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Sets P and Q are disjoint sets if the intersection of the two sets is a null set, P \u2229 Q = \u2205.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"P \u2229 Q \u2260 \u2205\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sets P and Q are disjoint sets if the intersection of the two sets is a null set, P \u2229 Q = \u2205.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"P$$\\\\cup$$Q = \u2205\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sets P and Q are disjoint sets if the intersection of the two sets is a null set, P \u2229 Q = \u2205.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"P$$\\\\cup$$Q \u2260 \u2205\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sets P and Q are disjoint sets if the intersection of the two sets is a null set, P \u2229 Q = \u2205.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"P \u2229 Q \u2260 \u2205\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Sets P and Q are disjoint sets if the intersection of the two sets is a null set, P \u2229 Q = \u2205.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Sets P and Q are disjoint sets if the intersection of the two sets is a null set, P \u2229 Q = \u2205.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-on-disjoint-sets\">Frequently Asked Questions on Disjoint Sets<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\" 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-0-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\"><strong>Is the empty set disjoint with itself?<\/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-0-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\">\n\n<p class=\"wp-block-paragraph\">Yes, the empty set is disjoint with itself.<\/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-1-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\"><strong>What is the cardinality of A B if A and B 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-1-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\">\n\n<p class=\"wp-block-paragraph\">n(A B) = n(A) + n(B) &#8211; n(AB)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If A and B are disjoint, n(AB) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, n(A B) = n(A) + n(B) if A and B are disjoint.<\/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-2-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\"><strong>What are mutually exclusive events in probability?<\/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-2-2fad97d5-556b-4ed9-8fc5-d8a2191ec63b\">\n\n<p class=\"wp-block-paragraph\">In probability theory, two events are said to be mutually exclusive if they cannot occur simultaneously (P(A $\\cap$ B) = 0). They are also called disjoint events.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Disjoint Sets? Disjoint sets are two sets that have no common elements. In other words, their intersection is the empty set. What does disjoint mean? The term disjoint simply means \u201cnot connected.\u201d So, disjoint sets are the non-intersecting sets; they have no elements in common.&nbsp; Example 1: Consider two sets: A = {2, &#8230; <a title=\"Disjoint Sets: Definition, Symbol, Facts, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/disjoint-sets\" aria-label=\"More on Disjoint Sets: Definition, Symbol, Facts, 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-34102","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\/34102","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=34102"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34102\/revisions"}],"predecessor-version":[{"id":34113,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34102\/revisions\/34113"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34102"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34102"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}