{"id":33940,"date":"2023-09-08T19:15:00","date_gmt":"2023-09-08T19:15:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33940"},"modified":"2023-09-11T07:38:41","modified_gmt":"2023-09-11T07:38:41","slug":"difference-of-sets-definition-venn-diagram-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/difference-of-sets","title":{"rendered":"Difference of Sets: Definition, Venn Diagram, 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-b9050dec-ba53-464e-86c9-93f9c138179b\" 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\/difference-of-sets#0-what-is-the-difference-of-sets>What Is the Difference of Sets?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/difference-of-sets#1-how-to-find-the-difference-of-sets>How to Find the Difference of Sets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/difference-of-sets#9-properties-of-difference-of-sets-and-complements>Properties of Difference of Sets and Complements<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/difference-of-sets#12-solved-examples-of-difference-of-sets>Solved Examples of Difference of Sets<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/difference-of-sets#13-practice-problems-on-set-difference>Practice Problems on Set Difference<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/difference-of-sets#14-frequently-asked-questions-on-set-difference>Frequently Asked Questions on Set Difference<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-difference-of-sets\">What Is the Difference of Sets?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The difference between the two sets, A and B, written as A \u2216 B or A \u2212 B, is a set that contains those elements of A that are NOT in B. To find the difference, we remove all the elements of set B from set A. The resulting set consists of the remaining elements exclusive to set A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We read A \u2212 B as \u201cA minus B.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u2212 B is a set obtained by eliminating the common elements between A and B from A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In simple words, the set A \u2212 B is a set obtained by removing the elements of A \u2229 B from A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We can define the difference between two sets using the set builder notation as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u2212B= {x : x \u2208 A and x \u2209 B}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B\u2212A= {x : x \u2208 B and x \u2209 A}<\/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\/calculate-the-difference-between-amounts-of-money\" 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\/measurement_sub_word_prob_2_pt.png\" alt=\"Calculate the Difference Between Amounts of Money 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\">Calculate the Difference Between Amounts of Money 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\/choose-the-correct-difference\" 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\/rec_add_sub_facts_find_missing_difference_6_pt.png\" alt=\"Choose the Correct Difference 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\">Choose the Correct Difference 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\/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\/cross-out-fractions-to-find-the-difference\" 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\/fractions_represent_sub_models_pt.png\" alt=\"Cross Out Fractions to Find the Difference 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\">Cross Out Fractions to Find the Difference 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\/cross-out-parts-to-find-the-difference-between-fractions\" 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\/fractions_represent_sub_greater_than_1_models_pt.png\" alt=\"Cross out Parts to Find the Difference Between Fractions 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\">Cross out Parts to Find the Difference Between Fractions 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\/cross-out-to-find-the-difference-between-a-mixed-number-and-a-fraction\" 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\/fractions_represent_sub_mixed_num_models_pt.png\" alt=\"Cross Out to FInd the Difference Between a Mixed Number and a Fraction 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\">Cross Out to FInd the Difference Between a Mixed Number and a Fraction 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\/determine-the-correct-difference\" 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\/rec_add_sub_facts_find_missing_difference_9_pt.png\" alt=\"Determine the Correct Difference 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\">Determine the Correct Difference 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\/determine-the-difference-and-match\" 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\/rec_add_sub_facts_mix_match_differences_7_pt.png\" alt=\"Determine the Difference and Match 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\">Determine the Difference and Match 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\/determine-the-difference\" 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\/rec_add_sub_facts_find_missing_difference_3_pt.png\" alt=\"Determine the Difference 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\">Determine the Difference 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\/determine-the-difference-to-match\" 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\/rec_add_sub_facts_mix_match_differences_8_pt.png\" alt=\"Determine the Difference to Match 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\">Determine the Difference to Match 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-how-to-find-the-difference-of-sets\">How to Find the Difference of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">To find the set difference between two sets, say Set A and Set B, follow the following steps:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1: <\/strong>Find the intersection of the sets A and B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2:<\/strong> Eliminate the elements of A \u2229 B from Set A to write a new set. In other words, remove the elements in A that are also present in Set B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3: <\/strong>Define the new set as A \u2212 B.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, B = {6, 7, 8, 9, 10, 11, 12}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u2229 B = {6, 7, 8, 9, 10}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;A \u2212 B = {<strong>1, 2, 3, 4, 5<\/strong>, <s>6, 7, 8, 9, 10<\/s>} \u2212 {<s>6, 7, 8, 9, 10<\/s>, 11, 12}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u2212 B = {1, 2, 3, 4, 5}<\/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\/difference-between-mixed-number-and-fraction\" 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\/difference-between-mixed-number-and-fraction.jpeg\" alt=\"Difference Between Mixed Number and Fraction Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/difference-of-mixed-numbers\" 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\/difference-of-mixed-numbers.jpeg\" alt=\"Difference of Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/difference-of-unlike-fractions-and-mixed-numbers\" 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\/difference-of-unlike-fractions-and-mixed-numbers.jpeg\" alt=\"Difference of Unlike Fractions and Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/difference-of-unlike-mixed-numbers\" 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\/difference-of-unlike-mixed-numbers.jpeg\" alt=\"Difference of Unlike Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/estimate-the-sum-or-the-difference\" 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\/estimate-the-sum-or-the-difference.jpeg\" alt=\"Estimate the Sum or the Difference Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-100\" 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\/even-difference-in-subtraction-expressions-within-100.jpeg\" alt=\"Even Difference in Subtraction Expressions Within 100\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-20\" 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\/even-difference-in-subtraction-expressions-within-20.jpeg\" alt=\"Even Difference in Subtraction Expressions Within 20\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/even-difference-in-subtraction-expressions-within-50\" 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\/even-difference-in-subtraction-expressions-within-50.jpeg\" alt=\"Even Difference in Subtraction Expressions Within 50\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-the-difference-by-making-10\" data-vars-ga-category=\"splashlearn_vocab\" 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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-order-of-the-difference-of-the-two-sets\">Order of the Difference of the Two Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">We know that order is important in subtraction. For example, 6-2 is not the same as 2-6. Similarly, the difference of sets is non-commutative.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It&#8217;s important to note that changing the order of the difference between two sets can lead to different results. So, for two sets A and B, the difference A &#8211; B may or may not be equal to B &#8211; A.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-difference-of-two-disjoint-sets\">Difference of Two Disjoint Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If A and B are disjoint sets, there are no common elements. So, when we define A &#8211; B, there are no elements to subtract or remove from the set A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A &#8211; B = A<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B &#8211; A = B<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-set-difference-in-venn-diagrams\">Set Difference in Venn Diagrams<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/venn-diagram\">Venn diagram<\/a> is the pictorial representation of sets and their different operations.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Observe the Venn diagram shown below.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Two circles that are overlapping symbolize sets A and B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The overlapping part shows the intersection of A and B.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The region of Set A that does not intersect with Set B represents A &#8211; B. The shaded area shows the elements that are exclusively found in Set A and are not present in Set B.<\/li>\n\n\n\n<li>The region of Set B that does not intersect with Set A represents B &#8211; A.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"470\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets.png\" alt=\"Venn Diagram of Set Difference\" class=\"wp-image-33946\" title=\"Venn Diagram of Set Difference\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets-300x227.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-finding-the-difference-of-sets-using-venn-diagram\">Finding the Difference of Sets Using Venn Diagram<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s consider an example to find the set difference between Set A = {1, 2, 3, 4, 5} and Set B = {3, 4, 5, 6, 7}.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s draw the Venn diagram.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"393\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets-venn-diagram.png\" alt=\"Venn diagram representation of the set difference A-B or A \\ B\" class=\"wp-image-33947\" title=\"Venn diagram representation of the set difference A-B or A \\ B\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets-venn-diagram.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets-venn-diagram-300x190.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A &#8211; B = {1, 2, 3, 4, 5} &#8211; {3, 4, 5, 6, 7} = {1, 2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B &#8211; A = {3, 4, 5, 6, 7} &#8211; {1, 2, 3, 4, 5} = {6, 7}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-difference-of-three-sets\">Difference of Three Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let A, B, and C are three non-empty sets, then the difference A \u2013 B \u2013 C represents the set that has the elements of A that are not in B and C.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"438\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets-three-intersecting-sets.png\" alt=\"Difference of three sets\" class=\"wp-image-33948\" title=\"Difference of three sets\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets-three-intersecting-sets.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/difference-of-sets-three-intersecting-sets-300x212.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-complement-of-a-set-and-difference-of-sets\">Complement of a Set and Difference of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The complement of a set is a new set that contains the elements not present in the given set (A) but belong to the universal set (U). The complement of a set is denoted by A&#8217; or A<sup>c<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The universal set is the set that includes all possible elements in a particular context. The complement of set A (A&#8217;) includes all elements in the universal set that are not present in A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In other words, we can define the complement of a set A as the difference between the sets U and A.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ac = U &#8211; A<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"458\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/complement-of-a-set.png\" alt=\"Complement of Set A or U - A\" class=\"wp-image-33949\" title=\"Complement of Set A or U - A\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/complement-of-a-set.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/complement-of-a-set-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Properties of Complement of a Set<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(A&#8217;)&#8217; = A<\/li>\n\n\n\n<li>A \u222a A&#8217; = U.<\/li>\n\n\n\n<li>A \u2229 A&#8217; = \u2205.<\/li>\n\n\n\n<li>De Morgan&#8217;s Laws:&nbsp;<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A&#8217; \u2229 B&#8217; = (A \u222a B)&#8217;<\/li>\n\n\n\n<li>A&#8217; \u222a B&#8217; =&nbsp; (A \u2229 B)&#8217;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example of Complement of a Set<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = {1, 3, 5, 7, 9}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Complement of A will contain the elements of U which are not present in A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u2019 = {2, 4, 6, 8, 10}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-symmetric-difference-of-sets\">Symmetric Difference of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The symmetric difference of two sets refers to an operation that gives a set that includes elements present in either of the two sets but absent in their intersection. It gives the elements that are found in set A or set B, but not in both A and B.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The symmetric difference is often denoted as A \u25b3 B or A \u229d B or A \u2295 B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u25b3 B = (A &#8211; B) \u222a (B &#8211; A)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It can also be calculated as given below:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u25b3 B = (A \u222a B) &#8211; (A \u2229 B)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, here in the symmetric difference, the elements unique to each set are combined, excluding the common ones that both the sets share.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"517\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/symmetric-difference-of-sets.png\" alt=\"Symmetric Difference of Sets\" class=\"wp-image-33951\" title=\"Symmetric Difference of Sets\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/symmetric-difference-of-sets.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/symmetric-difference-of-sets-300x250.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example of Symmetric Difference of Sets<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let us consider an example to show two sets to depict the symmetric difference:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Set A = {1, 2, 3, 4}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Set B = {3, 4, 5, 6}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We have to find the symmetric difference (A \u25b3 B) between Sets A and B.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s use the formula: (A &#8211; B) \u222a (B &#8211; A)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(A &#8211; B) = {1, 2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(B &#8211; A) = {5, 6}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lastly, combine these two sets found above:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(A &#8211; B) \u222a (B &#8211; A) = {1, 2} \u222a {5, 6}&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(A &#8211; B) \u222a (B &#8211; A) = {1, 2, 5, 6}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-properties-of-difference-of-sets-and-complements\">Properties of Difference of Sets and Complements<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When dealing with sets A and B, it is important to understand the properties of the difference between the two. Here, are some of them:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A &#8211; A = \u2205<\/li>\n\n\n\n<li>A &#8211; B = A \u2229 B<sup>c<\/sup><\/li>\n\n\n\n<li>\u2205 &#8211; A = \u2205<\/li>\n\n\n\n<li>A &#8211; \u2205 = A<\/li>\n\n\n\n<li>&nbsp;A \u2013 U = \u2205<\/li>\n\n\n\n<li>&nbsp;U \u2013 A = A\u2019<\/li>\n\n\n\n<li>A &#8211; B = B &#8211; A = \u2205 if A = B<\/li>\n\n\n\n<li>A &#8211; B = A if A \u2229 B = \u2205<\/li>\n\n\n\n<li>If A \u2282 B, then A &#8211; B = \u2205<\/li>\n\n\n\n<li>n(A \u0394 B) = n(A U B) &#8211; n(A \u2229 B)<\/li>\n\n\n\n<li>n(A \u0394 B) = n(A &#8211; B) + n(B &#8211; A)<\/li>\n\n\n\n<li>(A \u2229 B)\u2019 = A\u2019 \u222a B\u2019                       (DeMorgan\u2019s Law I)<\/li>\n\n\n\n<li>(A \u222a B)\u2019 = A\u2019 \u2229 B\u2019                       (DeMorgan\u2019s Law II)<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-facts-about-the-difference-of-sets\">Facts about the Difference of 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>A\u2212B= {x : x \u2208 A and x \u2209 B}<\/li>\n\n\n\n<li>B\u2212A= {x : x \u2208 B and x \u2209 A}<\/li>\n\n\n\n<li>The notation A &#8211; B shows the set acquired by removing the elements of A \u2229 B from A.<\/li>\n\n\n\n<li>The notation B &#8211; A shows the set acquired by removing the elements of A \u2229 B from B.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we learned about the concept of difference of sets, which involves creating a new set containing elements exclusive to one set while excluding those shared with another set. Understanding this fundamental operation in set theory allows us to manipulate and analyze sets effectively. Now, let&#8217;s put our knowledge into practice by solving examples and attempting MCQs to solidify our comprehension.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-solved-examples-of-difference-of-sets\">Solved Examples of Difference of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Given set A = {1, 2, 3, 4, 5} and set B = {3, 4, 5, 6, 7}. Find the difference between sets A and B.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = {1, 2, 3, 4, 5}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B = {3, 4, 5, 6, 7}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, the set difference A &#8211; B = {1, 2, 3, 4, 5} &#8211; {3, 4, 5, 6, 7}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A &#8211; B = {1, 2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. If X = {a, b, c, d, e} and Y = {c, d, e}, find X \\ Y.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X = {a, b, c, d, e}&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Set Y = {c, d, e}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X \\ Y means X &#8211; Y, the set of elements in set X that are not in set Y.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X \\ Y = {a, b}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. What is the set difference (P <\/strong>&#8211;<strong> Q) between Set P = {apple, banana, orange, pineapple} and Set Q = {banana, pineapple}?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P = {apple, banana, orange, pineapple}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q = {banana, pineapple}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P &#8211; Q is the set of elements in set P which are not present in Set Q. Remove the common elements between P and Q from the Set P.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P &#8211; Q = {apple, orange}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. What will be the complement set of Set A if A = {1, 2, 3, 4, 5} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = {1, 2, 3, 4, 5}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The complement of Set A is written as A&#8217;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A&#8217; = U &#8211; A<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A&#8217; = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} &#8211; {1, 2, 3, 4, 5}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A&#8217; = {6, 7, 8, 9, 10, 11, 12, 13, 14, 15}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5. Observe the Venn diagram and find&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>i) A&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>ii) B&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>iii) A <\/strong><strong>&#8211;<\/strong><strong> B.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"207\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram.png\" alt=\"venn diagram\" class=\"wp-image-33954\" title=\"venn diagram\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram.png 307w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/venn-diagram-300x202.png 300w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = {8, 10, 12, 14, 16}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B = {5, 7, 9, 11, 14, 16}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A &#8211; B is the set of elements from A that are not present in B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A &#8211; B = {8, 10, 12}<strong>&nbsp;<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-practice-problems-on-set-difference\">Practice Problems on Set Difference<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Difference of Sets: Definition, Venn Diagram, Examples<\/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\">Find A - B if A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{1, 2, 3}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{1, 2, 3, 4, 5, 6, 7, 8}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{6, 7, 8}<\/div><div class=\"spq_answer_block\" data-value=\"3\">{1, 2, 3, 6, 7, 8}<\/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: {1, 2, 3}<br\/>A - B = {1, 2, 3, 4, 5} - {4, 5, 6, 7, 8} = {1, 2, 3}.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find B - A if A = {red, blue, green} and B = {blue, green, yellow}.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{red, yellow}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{blue, green}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{yellow}<\/div><div class=\"spq_answer_block\" data-value=\"3\">{red}<\/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: {yellow}<br\/>B - A = {blue, green, yellow} - {red, blue, green} = {yellow}<\/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 = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Find A - B.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{1, 2}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{5, 6}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{3, 4, 5, 6}<\/div><div class=\"spq_answer_block\" data-value=\"3\">{1, 2, 5, 6}<\/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: {1, 2}<br\/>A - B = {1, 2, 3, 4} - {3, 4, 5, 6} = {1, 2}<\/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\">If  A = {a, b, c, d, e} and B = {c, d, f, g}, what is the set difference B \\ A?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{a, b, e}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{f, g}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{c, d, f, g}<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: {f, g}<br\/>There are common elements between A and B, which are c and d. If these elements are removed, the remaining items can be identified. On removing the common elements in both the sets, we are left with {f, g} in B.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">U - A = ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A \u2229 U<\/div><div class=\"spq_answer_block\" data-value=\"1\">A'<\/div><div class=\"spq_answer_block\" data-value=\"2\">A \u222a U<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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'<br\/>U - A = A'<\/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\": \"Difference of Sets: Definition, Venn Diagram, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Difference of Sets\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find A - 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A = {blue, green, yellow} - {red, blue, green} = {yellow}\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"{yellow}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"B - A = {blue, green, yellow} - {red, blue, green} = {yellow}\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"B - A = {blue, green, yellow} - {red, blue, green} = {yellow}\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. 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Find A - B.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A - B = {1, 2, 3, 4} - {3, 4, 5, 6} = {1, 2}\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{5, 6}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A - B = {1, 2, 3, 4} - {3, 4, 5, 6} = {1, 2}\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{3, 4, 5, 6}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A - B = {1, 2, 3, 4} - {3, 4, 5, 6} = {1, 2}\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{1, 2, 5, 6}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A - B = {1, 2, 3, 4} - {3, 4, 5, 6} = {1, 2}\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"{1, 2}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A - B = {1, 2, 3, 4} - {3, 4, 5, 6} = {1, 2}\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A - B = {1, 2, 3, 4} - {3, 4, 5, 6} = {1, 2}\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If  A = {a, b, c, d, e} and B = {c, d, f, g}, what is the set difference B \\\\ A?\",\n                    \"text\": \"If  A = {a, b, c, d, e} and B = {c, d, f, g}, what is the set difference B \\\\ A?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"There are common elements between A and B, which are c and d. If these elements are removed, the remaining items can be identified. On removing the common elements in both the sets, we are left with {f, g} in B.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{a, b, e}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are common elements between A and B, which are c and d. If these elements are removed, the remaining items can be identified. On removing the common elements in both the sets, we are left with {f, g} in B.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{c, d, f, g}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are common elements between A and B, which are c and d. If these elements are removed, the remaining items can be identified. On removing the common elements in both the sets, we are left with {f, g} in B.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are common elements between A and B, which are c and d. If these elements are removed, the remaining items can be identified. On removing the common elements in both the sets, we are left with {f, g} in B.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"{f, g}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"There are common elements between A and B, which are c and d. If these elements are removed, the remaining items can be identified. On removing the common elements in both the sets, we are left with {f, g} in B.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"There are common elements between A and B, which are c and d. If these elements are removed, the remaining items can be identified. On removing the common elements in both the sets, we are left with {f, g} in B.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"U - A = ?\",\n                    \"text\": \"U - A = ?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"U - A = A'\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A \u2229 U\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"U - A = A'\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A \u222a U\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"U - A = A'\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"U - A = A'\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"A'\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"U - A = A'\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"U - A = A'\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-frequently-asked-questions-on-set-difference\">Frequently Asked Questions on Set Difference<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-e2b8af85-09e7-412b-941e-99b0b8bdac1f\" 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-e2b8af85-09e7-412b-941e-99b0b8bdac1f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e2b8af85-09e7-412b-941e-99b0b8bdac1f\"><strong>What is the complement of the universal set?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-e2b8af85-09e7-412b-941e-99b0b8bdac1f\">\n\n<p class=\"wp-block-paragraph\">An empty set would be the complement of the universal set.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-e2b8af85-09e7-412b-941e-99b0b8bdac1f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e2b8af85-09e7-412b-941e-99b0b8bdac1f\"><strong>Are the sets A \u2013 B and B \u2013 A the same?<\/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-e2b8af85-09e7-412b-941e-99b0b8bdac1f\">\n\n<p class=\"wp-block-paragraph\">The difference of sets is not commutative. The sets<strong> <\/strong>A \u2013 B and B \u2013 A need not be equal.<\/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-e2b8af85-09e7-412b-941e-99b0b8bdac1f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e2b8af85-09e7-412b-941e-99b0b8bdac1f\"><strong>What is meant by A minus B in set theory?<\/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-e2b8af85-09e7-412b-941e-99b0b8bdac1f\">\n\n<p class=\"wp-block-paragraph\">In set theory, A minus B refers to the difference between A and B. In other words, it has the elements of Set A, which are not found in Set B.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Difference of Sets? The difference between the two sets, A and B, written as A \u2216 B or A \u2212 B, is a set that contains those elements of A that are NOT in B. To find the difference, we remove all the elements of set B from set A. The resulting &#8230; <a title=\"Difference of Sets: Definition, Venn Diagram, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/difference-of-sets\" aria-label=\"More on Difference of Sets: Definition, Venn Diagram, 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-33940","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\/33940","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=33940"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33940\/revisions"}],"predecessor-version":[{"id":33960,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33940\/revisions\/33960"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33940"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33940"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}