{"id":33163,"date":"2023-08-16T08:23:27","date_gmt":"2023-08-16T08:23:27","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33163"},"modified":"2023-08-19T18:41:50","modified_gmt":"2023-08-19T18:41:50","slug":"inverse-relation-definition-formula-graph-facts-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/inverse-relation","title":{"rendered":"Inverse Relation: Definition, Formula, Graph, 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-22097b22-0ca3-4060-9018-f1c9a0438d50\" 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\/inverse-relation#0-what-is-inverse-relation>What Is Inverse Relation?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/inverse-relation#2-inverse-relation-graph>Inverse Relation Graph<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/inverse-relation#5-domain-and-range-of-inverse-relation>Domain and Range of Inverse Relation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/inverse-relation#8-solved-example-on-inverse-relation>Solved Example on Inverse Relation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/inverse-relation#9-practice-problems-on-inverse-relation>Practice Problems on Inverse Relation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/inverse-relation#10-frequently-asked-questions-on-inverse-relation>Frequently Asked Questions on Inverse Relation<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-inverse-relation\">What Is Inverse Relation?<\/h2>\n\n\n\n<p><strong>An inverse relation is the inverse of a given relation obtained by Interchanging or swapping the elements of each ordered pair. In other words, if (x, y) is a point in a relation R, then (y, x) is an element in the inverse relation R<\/strong><strong><sup>\u20131<\/sup><\/strong><strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"402\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/inverse-relation.png\" alt=\"Inverse relation\" class=\"wp-image-33167\" title=\"Inverse relation\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/inverse-relation.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/inverse-relation-300x195.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>A relation R from set A to B is a subset of the Cartesian product of A and B. R is a subset of A $ \\times$ B. The elements of R of the form of an ordered pair (a, b) where a $\\in$ A and b $\\in$ B.<\/p>\n\n\n\n<p>The inverse relation of R is denoted by R<sup>\u20131<\/sup>. R<sup>\u20131<\/sup> is a subset of B $\\times$ A. The elements of R<sup>\u20131<\/sup>&nbsp; of the form of an ordered pair (b, a) where b $\\in$ B and a$\\in$ 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\/relationship-between-two-patterns\" 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\/algebra_analyze_relate_patterns_pt.png\" alt=\"Relationship Between Two Patterns 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\">Relationship Between Two Patterns 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-inverse-relation-definition\">Inverse Relation: Definition<\/h2>\n\n\n\n<p>Inverse relation is defined as the relation obtained by interchanging the elements of each ordered pair in the given relation. By swapping the inverse relation\u2019s domain and range, we can write the inverse relation.<\/p>\n\n\n\n<p>If R is a relation given by $R = \\left\\{(x,\\; y): x \u2208 A \\text{and} y \u2208 B\\right\\}$. then its inverse is given by&nbsp;<\/p>\n\n\n\n<p>$R^{-1} = \\left\\{(y,\\; x): y \u2208 B \\text{and} x \u2208 A\\right\\}$<\/p>\n\n\n\n<p>If R is a relation from set A to set B, then the inverse relationR<sup>\u20131<\/sup> is defined from set B to set A. In other words, if $(x,\\; y) \u2208 R$, then $(y,\\; x) \u2208 R^{-1}$ and vice versa.<\/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\/understand-the-relationship-in-division\" 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\/understand-the-relationship-in-division.jpeg\" alt=\"Understand the Relationship in Division 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-inverse-relation-graph\">Inverse Relation Graph<\/h2>\n\n\n\n<p>If the graph of a relation is given, its inverse can be found by reflecting it along the line $y = x$. To plot the inverse relation graph follow the following steps:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>On the given graph of a relation, select some points.<\/li>\n\n\n\n<li>To create new points, swap the x and y coordinates of each point.<\/li>\n\n\n\n<li>Draw a line connecting all of these new points, to get the graph of the inverse relation.<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s see an example of elements of a relation and inverse relation on a graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"661\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/inverse-relation-graph.png\" alt=\"Inverse relation graph\" class=\"wp-image-33169\" title=\"Inverse relation graph\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/inverse-relation-graph.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/inverse-relation-graph-281x300.png 281w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-inverse-relation-theorem\">Inverse Relation Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-2c98ed5f-81db-472d-a393-471fc7b6d59f\">\n\n\n<p><strong>Statement: <\/strong>The inverse relation theorem states that for any relation R, (R<sup>\u20131<\/sup>)<sup>\u20131<\/sup> = R.<\/p>\n\n\n<\/div>\n\n\n<p><strong>Proof:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Let\u2019s prove the inverse relation statement using the above-mentioned mathematical definition of relation and its inverse.<\/p>\n\n\n\n<p>If (x, y) \u2208 R, then (y, x) \u2208 R<sup>\u20131<\/sup> and vice versa.<\/p>\n\n\n\n<p>Let (x, y) \u2208 R \u21d4 (y, x) \u2208 R<sup>\u20131<\/sup><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u21d4 (x, y) \u2208 (R<sup>\u20131<\/sup>)<sup>\u20131<\/sup><\/p>\n\n\n\n<p>Every element of R is in (R<sup>\u20131<\/sup>)<sup>\u20131<\/sup>.&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>Thus, R $\\subseteq$ (R<sup>\u20131<\/sup>)<sup>\u20131 <\/sup>&nbsp;<\/p>\n\n\n\n<p>Also, following the reverse steps, we get that every element in (R<sup>\u20131<\/sup>)<sup>\u20131 <\/sup>is in R.<\/p>\n\n\n\n<p>Thus, (R<sup>\u20131<\/sup>)<sup>\u20131<\/sup> $\\subseteq$ R<\/p>\n\n\n\n<p>Hence,&nbsp; (R<sup>\u20131<\/sup>)<sup>\u20131<\/sup> = R.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-inverse-of-algebraic-relation\">Inverse of Algebraic Relation<\/h2>\n\n\n\n<p>If an algebraic form of a relation is given, such as R $= \\left\\{(x,\\; y): y = ax + b\\right\\}$.<\/p>\n\n\n\n<p>Then the steps listed below are used to find its inverse.<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Interchange or swap the variables x and y.<\/p>\n\n\n\n<p>For the given algebraic equation, after interchanging variables, x = ay + b<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Now express y in terms of x.<\/p>\n\n\n\n<p>Here, x = ay + b<\/p>\n\n\n\n<p>$\\Rightarrow ay = x \\;-\\; b$<\/p>\n\n\n\n<p>$y = \\frac{x \\;-\\; b}{a}$<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Then write the given algebraic relation\u2019s inverse as<\/p>\n\n\n\n<p>&nbsp;&nbsp;R<sup>\u20131<\/sup> $= \\left\\{(x,\\; y): y = \\frac{x \\;-\\ b}{a} \\right\\}$<\/p>\n\n\n\n<p><strong>Note<\/strong>: Check to see if the graphs y = ax + b and $y = \\frac{x \\;-\\; b}{a}$ are symmetric about the line y = x.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-domain-and-range-of-inverse-relation\">Domain and Range of Inverse Relation<\/h2>\n\n\n\n<p>The domain and range of a given relation are interchanged when we find the inverse relation.<\/p>\n\n\n\n<p><strong>Domain:&nbsp;<\/strong><\/p>\n\n\n\n<p>The set of all first elements of the ordered pairs of R is referred to as the domain of a relation.&nbsp; The range of R is then the domain of R<sup>\u20131<\/sup>.<\/p>\n\n\n\n<p><strong>Range:&nbsp;<\/strong><\/p>\n\n\n\n<p>The set of all the second element sets is referred to as the range of the relation R. The domain of R is then the range of R<sup>\u20131<\/sup>.<\/p>\n\n\n\n<p><strong>Example:<\/strong>&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Relation<\/strong><\/th><th><strong>Inverse<\/strong><\/th><\/tr><\/thead><tbody><tr><td>R $= \\left\\{(2, 4), (4, 16), (6, 36)\\right\\}$<\/td><td>R<sup>\u20131<\/sup> $= \\left\\{(4, 2), (16, 4), (36, 6)\\right\\}$<\/td><\/tr><tr><td>Domain of relation R $= \\left\\{2,4,6\\right\\}$.<\/td><td>Domain of relation R $= \\left\\{4,16,36\\right\\}$.<\/td><\/tr><tr><td>Range of relation R $= \\left\\{4,16,36\\right\\}.$<\/td><td>Range of relation R $= \\left\\{2,4,6\\right\\}$&nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-inverse-relation\">Facts about Inverse Relation<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>If R is a symmetric relation, then R = R<sup>\u20131<\/sup>.<\/li>\n\n\n\n<li>The curves that represent a relation and its inverse on a graph are symmetric around the line y = x.<\/li>\n\n\n\n<li>Every function is a relation. Not every relation is a function. In a function, each input (domain element) is associated with exactly one output (range element), while in a general relation, an input can be associated with multiple outputs.<\/li>\n\n\n\n<li>If the original relation has a positive slope, the inverse relation will have a negative slope, and vice versa.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have learned the inverse relation definition, their graph, the inverse of algebraic relation, domain, range of inverse relation. Let\u2019s solve a few examples.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-example-on-inverse-relation\">Solved Example on Inverse Relation<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Write the inverse of the relation <\/strong><strong>R = {(1, x), (2, y), (3, z)}<\/strong><strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>R = {(1, x), (2, y), (3, z)}<\/strong><\/p>\n\n\n\n<p>The inverse of the relation is obtained by interchanging the elements of each ordered pair in a relation.<\/p>\n\n\n\n<p>Hence, $R^{-1}$ = {(x,1),(y,2),(z,3)}.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>Find the domain and range of a relation R = <\/strong>{ (x, $x^{3}$)<strong>: x is an odd number less than 10}.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>R = { (x, $x^{3}$): x is an odd number less than 10}.<\/p>\n\n\n\n<p>Odd numbers less than 10 are 1, 3, 5, 7, 9.<\/p>\n\n\n\n<p>R = {(1, 1<sup>3<\/sup>),(3, 3<sup>3<\/sup>), (5, 5<sup>3<\/sup>), (7, 7<sup>3<\/sup>), (9, 9<sup>3<\/sup>)}<\/p>\n\n\n\n<p>R = {(1, 1), (3, 27), (5, 125), (7, 343), (9, 729)}<\/p>\n\n\n\n<p>Domain of R = {1, 3, 5, 7, 9}<\/p>\n\n\n\n<p>Range of R = {1, 27, 125, 343, 729}<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>If a relation is given by R = {(x, y); y = 2x + 3,<\/strong>1$\\le x \\le$ 4<strong>}, the domain and range of its inverse relation.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>R = {(x, y); y = 2x + 3,<\/strong>$1 \\le x \\le 4$<strong>}<\/strong><\/p>\n\n\n\n<p>For x = 1, y = 5<\/p>\n\n\n\n<p>For x = 2, y = 7<\/p>\n\n\n\n<p>For x = 3, y = 9<\/p>\n\n\n\n<p>For x = 4, y = 11<\/p>\n\n\n\n<p>R = {(1, 5), (2, 7), (3, 9), (4, 11)}<\/p>\n\n\n\n<p>Hence, R<sup>\u20131<\/sup> = {(5, 1), (7, 2), (9, 3), (11, 4)}<\/p>\n\n\n\n<p>Domain of R<sup>\u20131<\/sup>&nbsp; = {1, 2, 3, 4}<\/p>\n\n\n\n<p>Range of R<sup>\u20131<\/sup>&nbsp; = {5, 7, 9, 11}<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-inverse-relation\">Practice Problems on Inverse Relation<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Inverse Relation: Definition, Formula, Graph, 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\">The graphs of a relation and its inverse relation are symmetrical along ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">y = x<\/div><div class=\"spq_answer_block\" data-value=\"1\">y = \u2013 x<\/div><div class=\"spq_answer_block\" data-value=\"2\">y = x + 1<\/div><div class=\"spq_answer_block\" data-value=\"3\">y = \u2013 x +1<\/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: y = x<br\/>The graph of inverse relation is symmetrical in y = x.<\/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\">The domain of an inverse relation $R^{\u20131}$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)}<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{1, 2, 3, 4, 5}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{0.1, 0.2, 0.3, 0.4, 0.5}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)}<\/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: {0.1, 0.2, 0.3, 0.4, 0.5}<br\/>The set of first elements of all ordered pairs is called domain.<br>\r\nHence, the domain of $R^{\u20131}$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)} is {0.1, 0.2, 0.3, 0.4, 0.5}<\/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\">What is the range of the inverse relation of R = {(1, a), (2, b), (3, c), (4, d), (5, e)}?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{1, 2, 3, 4, 5}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{a, b, c, d, e}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{(a,1),(b, 2), (c, 3), (d, 4), (e, 5)}<\/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: {1, 2, 3, 4, 5}<br\/>Given, R = {(1, a), (2, b), (3, c), (4, d), (5, e)}<br>\r\nInverse relation of R is given by,<br>\r\n$R^{-1} = {(a,1)(b,2),(c,3),(d,4),(e,5)}<br>\r\nThe set of second elements of all ordered pairs is called range.<br>\r\nHence, range={1, 2, 3, 4, 5}<\/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\">Let $y = \\frac{1}{x}$. What is the inverse relation of y?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$f^{\u20131}$(x) = \u2013 x<\/div><div class=\"spq_answer_block\" data-value=\"1\">$f^{\u20131}(x) = \\frac{1}{x}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$f^{\u20131}$(x) = x<\/div><div class=\"spq_answer_block\" data-value=\"3\">$f^{\u20131}(x) = \\;-\\; \\frac{1}{x}$<\/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: $f^{\u20131}(x) = \\frac{1}{x}$<br\/>To find the inverse relation of h, we need to swap the variables x and y and solve for y. So, we start by writing:<br>\r\n$x = \\frac{1}{y}$<br>\r\n$y = \\frac{1}{x}$<br>\r\nTherefore, the inverse relation of y is $f^{\u20131}(x) = \\frac{1}{x}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The range of inverse relation $R^{\u20131} = {(x,1): x is a natural number less than 7} is____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">{1}<\/div><div class=\"spq_answer_block\" data-value=\"1\">{0}<\/div><div class=\"spq_answer_block\" data-value=\"2\">{1, 2, 3, 4, 5, 6}<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: {1}<br\/>$R^{\u20131}$ = {(x,1): x is a natural number less than 7}<br>\r\n$\\Rightarrow R^{\u20131}$ = {(1,1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}<br>\r\nRange of $R^{\u20131}$ = {1}<\/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\": \"Inverse Relation: Definition, Formula, Graph, Facts, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Inverse Relation\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n          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\"Comment\",\n                                    \"text\": \"The graph of inverse relation is symmetrical in y = x.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"y = x + 1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The graph of inverse relation is symmetrical in y = x.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"y = \u2013 x +1\",\n                                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\"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The domain of an inverse relation $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)}\",\n                    \"text\": \"The domain of an inverse relation $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)}\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The set of first elements of all ordered pairs is called domain.<br>\r\nHence, the domain of $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)} is {0.1, 0.2, 0.3, 0.4, 0.5}\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{1, 2, 3, 4, 5}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The set of first elements of all ordered pairs is called domain.<br>\r\nHence, the domain of $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)} is {0.1, 0.2, 0.3, 0.4, 0.5}\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The set of first elements of all ordered pairs is called domain.<br>\r\nHence, the domain of $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)} is {0.1, 0.2, 0.3, 0.4, 0.5}\"\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\": \"The set of first elements of all ordered pairs is called domain.<br>\r\nHence, the domain of $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)} is {0.1, 0.2, 0.3, 0.4, 0.5}\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"{0.1, 0.2, 0.3, 0.4, 0.5}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The set of first elements of all ordered pairs is called domain.<br>\r\nHence, the domain of $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)} is {0.1, 0.2, 0.3, 0.4, 0.5}\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The set of first elements of all ordered pairs is called domain.<br>\r\nHence, the domain of $$R^{\u20131}$$ = {(0.1, 1), (0.2, 2), (0.3, 3), (0.4, 4), (0.5, 5)} is {0.1, 0.2, 0.3, 0.4, 0.5}\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the range of the inverse relation of R = {(1, a), (2, b), (3, c), (4, d), (5, e)}?\",\n                    \"text\": \"What is the range of the inverse relation of R = {(1, a), (2, b), (3, c), (4, d), (5, e)}?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Given, R = {(1, a), (2, b), (3, c), (4, d), (5, e)}<br>\r\nInverse relation of R is given by,<br>\r\n$$R^{-1} = {(a,1)(b,2),(c,3),(d,4),(e,5)}<br>\r\nThe set of second elements of all ordered pairs is called range.<br>\r\nHence, range={1, 2, 3, 4, 5}\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{a, b, c, d, e}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given, R = {(1, a), (2, b), (3, c), (4, d), (5, e)}<br>\r\nInverse relation of R is given by,<br>\r\n$$R^{-1} = {(a,1)(b,2),(c,3),(d,4),(e,5)}<br>\r\nThe set of second elements of all ordered pairs is called range.<br>\r\nHence, range={1, 2, 3, 4, 5}\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{(a,1),(b, 2), (c, 3), (d, 4), (e, 5)}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given, R = {(1, a), (2, b), (3, c), (4, d), (5, e)}<br>\r\nInverse relation of R is given by,<br>\r\n$$R^{-1} = {(a,1)(b,2),(c,3),(d,4),(e,5)}<br>\r\nThe set of second elements of all ordered pairs is called range.<br>\r\nHence, range={1, 2, 3, 4, 5}\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Given, R = {(1, a), (2, b), (3, c), (4, d), (5, e)}<br>\r\nInverse relation of R is given by,<br>\r\n$$R^{-1} = {(a,1)(b,2),(c,3),(d,4),(e,5)}<br>\r\nThe set of second elements of all ordered pairs is called range.<br>\r\nHence, range={1, 2, 3, 4, 5}\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"{1, 2, 3, 4, 5}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Given, R = {(1, a), (2, b), (3, c), (4, d), (5, e)}<br>\r\nInverse relation of R is given by,<br>\r\n$$R^{-1} = {(a,1)(b,2),(c,3),(d,4),(e,5)}<br>\r\nThe set of second elements of all ordered pairs is called range.<br>\r\nHence, range={1, 2, 3, 4, 5}\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Given, R = {(1, a), (2, b), (3, c), (4, d), (5, e)}<br>\r\nInverse relation of R is given by,<br>\r\n$$R^{-1} = {(a,1)(b,2),(c,3),(d,4),(e,5)}<br>\r\nThe set of second elements of all ordered pairs is called range.<br>\r\nHence, range={1, 2, 3, 4, 5}\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Let $$y = \\\\frac{1}{x}$$. What is the inverse relation of y?\",\n                    \"text\": \"Let $$y = \\\\frac{1}{x}$$. What is the inverse relation of y?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"To find the inverse relation of h, we need to swap the variables x and y and solve for y. So, we start by writing:<br>\r\n$$x = \\\\frac{1}{y}$$<br>\r\n$$y = \\\\frac{1}{x}$$<br>\r\nTherefore, the inverse relation of y is $$f^{\u20131}(x) = \\\\frac{1}{x}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$f^{\u20131}$$(x) = \u2013 x\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To find the inverse relation of h, we need to swap the variables x and y and solve for y. So, we start by writing:<br>\r\n$$x = \\\\frac{1}{y}$$<br>\r\n$$y = \\\\frac{1}{x}$$<br>\r\nTherefore, the inverse relation of y is $$f^{\u20131}(x) = \\\\frac{1}{x}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$f^{\u20131}$$(x) = x\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To find the inverse relation of h, we need to swap the variables x and y and solve for y. So, we start by writing:<br>\r\n$$x = \\\\frac{1}{y}$$<br>\r\n$$y = \\\\frac{1}{x}$$<br>\r\nTherefore, the inverse relation of y is $$f^{\u20131}(x) = \\\\frac{1}{x}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$f^{\u20131}(x) = \\\\;-\\\\; \\\\frac{1}{x}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To find the inverse relation of h, we need to swap the variables x and y and solve for y. So, we start by writing:<br>\r\n$$x = \\\\frac{1}{y}$$<br>\r\n$$y = \\\\frac{1}{x}$$<br>\r\nTherefore, the inverse relation of y is $$f^{\u20131}(x) = \\\\frac{1}{x}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$f^{\u20131}(x) = \\\\frac{1}{x}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"To find the inverse relation of h, we need to swap the variables x and y and solve for y. So, we start by writing:<br>\r\n$$x = \\\\frac{1}{y}$$<br>\r\n$$y = \\\\frac{1}{x}$$<br>\r\nTherefore, the inverse relation of y is $$f^{\u20131}(x) = \\\\frac{1}{x}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"To find the inverse relation of h, we need to swap the variables x and y and solve for y. So, we start by writing:<br>\r\n$$x = \\\\frac{1}{y}$$<br>\r\n$$y = \\\\frac{1}{x}$$<br>\r\nTherefore, the inverse relation of y is $$f^{\u20131}(x) = \\\\frac{1}{x}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The range of inverse relation $$R^{\u20131} = {(x,1): x is a natural number less than 7} is____.\",\n                    \"text\": \"The range of inverse relation $$R^{\u20131} = {(x,1): x is a natural number less than 7} is____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$R^{\u20131}$$ = {(x,1): x is a natural number less than 7}<br>\r\n$$\\\\Rightarrow R^{\u20131}$$ = {(1,1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}<br>\r\nRange of $$R^{\u20131}$$ = {1}\"\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\": \"$$R^{\u20131}$$ = {(x,1): x is a natural number less than 7}<br>\r\n$$\\\\Rightarrow R^{\u20131}$$ = {(1,1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}<br>\r\nRange of $$R^{\u20131}$$ = {1}\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"{1, 2, 3, 4, 5, 6}\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$R^{\u20131}$$ = {(x,1): x is a natural number less than 7}<br>\r\n$$\\\\Rightarrow R^{\u20131}$$ = {(1,1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}<br>\r\nRange of $$R^{\u20131}$$ = {1}\"\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\": \"$$R^{\u20131}$$ = {(x,1): x is a natural number less than 7}<br>\r\n$$\\\\Rightarrow R^{\u20131}$$ = {(1,1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}<br>\r\nRange of $$R^{\u20131}$$ = {1}\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"{1}\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$R^{\u20131}$$ = {(x,1): x is a natural number less than 7}<br>\r\n$$\\\\Rightarrow R^{\u20131}$$ = {(1,1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}<br>\r\nRange of $$R^{\u20131}$$ = {1}\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$R^{\u20131}$$ = {(x,1): x is a natural number less than 7}<br>\r\n$$\\\\Rightarrow R^{\u20131}$$ = {(1,1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}<br>\r\nRange of $$R^{\u20131}$$ = {1}\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-on-inverse-relation\">Frequently Asked Questions on Inverse Relation<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-9869f16e-1dab-4804-a451-db02b66558ec\" 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-0-9869f16e-1dab-4804-a451-db02b66558ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9869f16e-1dab-4804-a451-db02b66558ec\"><strong>What is an inverse relation?<\/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-0-9869f16e-1dab-4804-a451-db02b66558ec\">\n\n<p>An inverse relation of a given relation is a relation where the order of the pairs is reversed. If the set of ordered pairs in the original relation is (a, b), the set of ordered pairs in the inverse relation is (b, a).<\/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-1-9869f16e-1dab-4804-a451-db02b66558ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9869f16e-1dab-4804-a451-db02b66558ec\"><strong>What do you mean by the domain of relation?<\/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-1-9869f16e-1dab-4804-a451-db02b66558ec\">\n\n<p>The domain of a relation is the set that contains all of the first elements of all ordered pairs in the relation R.<\/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-2-9869f16e-1dab-4804-a451-db02b66558ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9869f16e-1dab-4804-a451-db02b66558ec\"><strong>What is an empty relation?<\/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-2-9869f16e-1dab-4804-a451-db02b66558ec\">\n\n<p>An empty relation is one in which there is no relation between any elements of a set.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-9869f16e-1dab-4804-a451-db02b66558ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9869f16e-1dab-4804-a451-db02b66558ec\"><strong>What is the range of relation?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-9869f16e-1dab-4804-a451-db02b66558ec\">\n\n<p>The set of the second coordinates from the ordered pair in a relation is called range.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-9869f16e-1dab-4804-a451-db02b66558ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9869f16e-1dab-4804-a451-db02b66558ec\"><strong>What is the symmetric relation?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-9869f16e-1dab-4804-a451-db02b66558ec\">\n\n<p>A relation R defined on the set A is said to be symmetric if (b, a)$\\in$ R holds true when (a, b) $\\in$ R, for all a and b in A.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Inverse Relation? An inverse relation is the inverse of a given relation obtained by Interchanging or swapping the elements of each ordered pair. In other words, if (x, y) is a point in a relation R, then (y, x) is an element in the inverse relation R\u20131. A relation R from set A &#8230; <a title=\"Inverse Relation: Definition, Formula, Graph, Facts, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/inverse-relation\" aria-label=\"More on Inverse Relation: Definition, Formula, Graph, 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-33163","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\/33163","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=33163"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33163\/revisions"}],"predecessor-version":[{"id":33220,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33163\/revisions\/33220"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33163"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33163"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33163"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}