{"id":30842,"date":"2023-06-19T09:46:19","date_gmt":"2023-06-19T09:46:19","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=30842"},"modified":"2023-11-16T05:05:55","modified_gmt":"2023-11-16T05:05:55","slug":"reflexive-property-definition-equality-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/reflexiv-property","title":{"rendered":"Reflexive Property &#8211; Definition, Equality, 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-9281cc4b-133f-4733-a089-07318c10fa3a\" 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\/reflexiv-property#0-what-is-reflexive-property>What Is Reflexive Property?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reflexiv-property#2-reflexive-property-of-equality>Reflexive Property of Equality<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reflexiv-property#3-reflexive-property-of-relations>Reflexive Property of Relations<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reflexiv-property#6-solved-examples-of-reflexive-property>Solved Examples of Reflexive Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reflexiv-property#7-practice-problems-on-reflexive-property>Practice Problems on Reflexive Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/reflexiv-property#8-frequently-asked-questions-about-reflexive-property>Frequently Asked Questions about Reflexive Property<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-reflexive-property\">What Is Reflexive Property?<\/h2>\n\n\n\n<p><strong>Reflexive property is a fundamental property of relations which states that every element of a set is related to itself by that relation. Mathematically, a relation R on a set A is said to be reflexive if for all a \u2208 A, (a, a) \u2208 R.<\/strong><\/p>\n\n\n\n<p>You can think of the reflexive property as finding a reflection of yourself in a mirror. The reflexive property on a set states that every component\/element is related to itself. In the case of congruence, it is known as the reflexive property of congruence. If the case is of equality, it is known as the reflexive property of equality.&nbsp;<\/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\/add-using-associative-property\" 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\/add_sub_facts_together_we_flee_4_gm.png\" alt=\"Add Using Associative Property 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\">Add Using Associative Property 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\/apply-distributive-property\" 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\/mult_div_facts_mul_dispro_exp1_pt.png\" alt=\"Apply Distributive Property 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\">Apply Distributive Property 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\/multiply-using-the-commutative-property\" 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\/mult_div_facts_mul_compro_fact2_pt.png\" alt=\"Multiply using the Commutative Property 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\">Multiply using the Commutative Property 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\/solve-using-distributive-property\" 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\/mult_div_facts_mul_dispro_pProd_pt.png\" alt=\"Solve using Distributive Property 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\">Solve using Distributive Property 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 = 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-reflexive-property-of-congruence\">Reflexive Property of Congruence<\/h2>\n\n\n\n<p><strong>The reflexive property of congruence states that every geometric shape or geometric figure is congruent to itself.&nbsp;<\/strong><\/p>\n\n\n\n<p>When two shapes have the same size and shape, they are said to be congruent. The symbol for congruence is \u2245. Reflexive property in <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometry\">geometry<\/a> is pretty easy to understand.<\/p>\n\n\n\n<p><strong>Reflexive property of congruence examples:<\/strong><\/p>\n\n\n\n<p>By the reflexive property of segment congruence, we can say that every line segment is congruent to itself.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"489\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/reflexive-property-of-congruence-examples.png\" alt=\"\" class=\"wp-image-36004\" title=\"Reflexive property of congruence examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/reflexive-property-of-congruence-examples.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/reflexive-property-of-congruence-examples-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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\/add-the-numbers-using-commutative-property-of-addition\" 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\/add-the-numbers-using-commutative-property-of-addition.jpeg\" alt=\"Add the Numbers Using Commutative Property of Addition\">\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\/apply-commutative-property-of-addition\" 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\/apply-commutative-property-of-addition.jpeg\" alt=\"Apply Commutative Property of Addition 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\/apply-commutative-property\" 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\/apply-commutative-property.jpeg\" alt=\"Apply Commutative Property 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\/apply-distributive-property-in-2-different-ways\" 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\/apply-distributive-property-in-2-different-ways.jpeg\" alt=\"Apply Distributive Property in 2 Different Ways 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\/apply-the-commutative-property-of-addition\" 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\/apply-the-commutative-property-of-addition.jpeg\" alt=\"Apply the Commutative Property of Addition 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\/break-it-down-using-distributive-property\" 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src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-multiply-add-using-distributive-property.jpeg\" alt=\"Break Multiply Add using Distributive Property 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\/break-using-distributive-property\" 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\/break-using-distributive-property.jpeg\" alt=\"Break using Distributive Property 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\/commutative-property-of-addition-on-number-line\" 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\/commutative-property-of-addition-on-number-line.jpeg\" alt=\"Commutative Property of Addition on Number Line 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\/commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" 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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-reflexive-property-of-equality\">Reflexive Property of Equality<\/h2>\n\n\n\n<p><strong>The reflexive property of equality states that every number is equal to itself. For any number a, we have <\/strong>$a = a$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Examples:&nbsp;<\/strong><\/p>\n\n\n\n<p>$1 = 1$<\/p>\n\n\n\n<p>$\\;-\\;7 = \\;-\\;7$<\/p>\n\n\n\n<p>$x = x$<\/p>\n\n\n\n<p>Define the relation of equality on the set of real numbers as R such that <strong>a R b<\/strong> if and only if <strong>a = b<\/strong>.<\/p>\n\n\n\n<p>The relation R is an equivalence relation since it is reflexive, symmetric, and transitive.<\/p>\n\n\n\n<p>i) Reflexive property: $a = a$<\/p>\n\n\n\n<p>ii) Symmetric property: If $a = b$, then $b = a$.<\/p>\n\n\n\n<p>iii) Transitive property: If $a = b$ and $b = c$, then $a = c$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-reflexive-property-of-relations\">Reflexive Property of Relations<\/h2>\n\n\n\n<p><strong>A binary relation R defined on a set A is said to be reflexive if, for every element a \u2208 A, we have aRa, that is, (a, a) \u2208 R. If R is a reflexive relation on a set A, then every element of A is related to itself by R.<\/strong><\/p>\n\n\n\n<p>An example of the relation \u201cis equal to.\u201d It is reflexive as every number is equal to itself. Also, the reflexive property of congruence and equality are ultimate cases of reflexive property of relations. An example of the reflexive property of equality is \u201cis a subset of,\u201d as we know, every set is a subset of itself.<\/p>\n\n\n\n<p><strong>Example: Is the relation <\/strong>$R = \\left\\{ (1,\\; 1),\\; (2,\\; 2),\\; (1,\\; 2) \\right\\}$<strong> defined on the set <\/strong>$\\left\\{1, 2\\right\\}$<strong> reflexive?<\/strong><\/p>\n\n\n\n<p>1 R 1 since (1, 1) \u2208 R<\/p>\n\n\n\n<p>2 R 2 since (2, 2) \u2208 R<\/p>\n\n\n\n<p>Each element in the set is related to itself. Thus, the relation is reflexive.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-reflexive-property\">Facts about Reflexive Property<\/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>In mathematical terms, the reflexive property simply states that $a = a$ where \u201ca\u201d is a real number.<\/li>\n\n\n\n<li>We can find applications of the reflexive property in different mathematical proofs and operations.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the reflexive property, reflexive property of equality, and reflexive property of congruence. Let\u2019s solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-of-reflexive-property\">Solved Examples of Reflexive Property<\/h2>\n\n\n\n<p><strong>1. Is the relation <\/strong>$R = \\left\\{ (a,\\; a),\\; (a,\\; b),\\; (b,\\; b) \\right\\}$<strong> defined on the set <\/strong>$A = \\left\\{a,\\; b,\\; c\\right\\}$<strong> reflexive?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$A = \\left\\{a,\\; b,\\; c\\right\\}$<\/p>\n\n\n\n<p>$R = \\left\\{ (a,\\; a),\\; (a,\\; b),\\; (b,\\; b) \\right\\}$<\/p>\n\n\n\n<p>a R a since&nbsp; (a, a) \u2208 R<\/p>\n\n\n\n<p>b R b since (b, b) \u2208 R<\/p>\n\n\n\n<p>(c, c) R<\/p>\n\n\n\n<p>Thus, the element c is not related to itself.<\/p>\n\n\n\n<p>The relation R is not reflexive.<\/p>\n\n\n\n<p><strong>2. A binary relation R is defined on the set of real numbers. For natural numbers a and b, we have <em>a R b<\/em> if and only if <\/strong><em>$<\/em>a \\lt b$<strong><em>.<\/em> Is the relation reflexive?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>A relation is said to be reflexive if every element of the set is related to itself.<\/p>\n\n\n\n<p>The \u201cless than $(\\lt)$\u201d relation is not reflexive because a number can never be less than itself.<\/p>\n\n\n\n<p>For any real number, the statement $a \\lt a$ is not true.<\/p>\n\n\n\n<p>Thus, R is not reflexive.<\/p>\n\n\n\n<p><strong>3. What does the reflexive property of congruence state for a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/line-segment\"><strong>line segment<\/strong><\/a><strong> PQ, an <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\"><strong>angle<\/strong><\/a><strong> X, and a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\"><strong>triangle<\/strong><\/a><strong> ABC.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Reflexive property of congruence states that every geometric figure is congruent to itself.<\/p>\n\n\n\n<p>PQ \u2245 PQ<\/p>\n\n\n\n<p>\u2220X \u2245 \u2220X<\/p>\n\n\n\n<p>ABC \u2245 ABC<\/p>\n\n\n\n<p><strong>4. Observe the diagram below and write statements based on the reflexive property.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"257\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/two-congruent-triangles.png\" alt=\"Two congruent triangles\" class=\"wp-image-36005\" style=\"width:269px;height:257px\" title=\"Two congruent triangles\"\/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Every triangle is congruent to itself.<\/p>\n\n\n\n<p>AOB \u2245 AOB<\/p>\n\n\n\n<p>&nbsp;POQ \u2245 POQ<\/p>\n\n\n\n<p>Every line segment is congruent to itself.<\/p>\n\n\n\n<p>OA \u2245 OA, OB \u2245 OB, AB \u2245 AB<\/p>\n\n\n\n<p>OP \u2245 OP, OQ \u2245 OQ, PQ \u2245 PQ<\/p>\n\n\n\n<p>Every angle is congruent to itself.<\/p>\n\n\n\n<p>\u2220A \u2245 \u2220A, \u2220B \u2245 \u2220B,\u2220O \u2245 \u2220O, \u2220P \u2245 \u2220P, \u2220Q \u2245 \u2220Q<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-reflexive-property\">Practice Problems on Reflexive Property<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Reflexive Property - Definition, Equality, 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\">Which statement is NOT based on the reflexive property of equality?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$0 = 0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\;-\\;9 = \\;-\\;9$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x = x$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$a = \\;-\\;8$<\/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: $0 = 0$<br\/>Reflexive property of equality for real numbers states that $a = a$, for any real number a.<br>\r\nThe statement $a = \\;-\\;8$ simply states that the value of the variable a is $\\;-\\;8$. It is not based on the reflexive property of equality.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">For any real number r, the statement $r = r$ is based on the<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Reflexive property of equality<\/div><div class=\"spq_answer_block\" data-value=\"1\">Reflexive property of congruence<\/div><div class=\"spq_answer_block\" data-value=\"2\">Symmetric property<\/div><div class=\"spq_answer_block\" data-value=\"3\">Transitive property<\/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: Reflexive property of equality<br\/>By the reflexive property of equality, every real number \u201cr\u201d is equal to itself.<br>\r\nIt can be denoted as$ r = r$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following expressions is NOT based on the reflexive property of congruence?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\Delta ABC \\cong \\Delta ABC$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$XY \\cong XY$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\angle A \\cong \\angle A$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$| (AB) = | (BA)$<\/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: $| (AB) = | (BA)$<br\/>By the reflexive property of congruence, every geometric figure (an angle, line segment, or shape) is congruent to itself.<br>\r\n$| (AB) = | (BA)$ simply means that the length of the line segment remains the same. This is true regardless of the order of endpoints you choose to help name the segment. It is not based on the reflexive property of congruence.<\/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\": \"Reflexive Property - Definition, Equality, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Reflexive Property\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which statement is NOT based on the reflexive property of equality?\",\n                    \"text\": \"Which statement is NOT based on the reflexive property of equality?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Reflexive property of equality for real numbers states that $$a = a$$, for any real number a.<br>\r\nThe statement $$a = \\\\;-\\\\;8$$ simply states that the value of the variable a is $$\\\\;-\\\\;8$$. It is not based on the reflexive property of equality.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;9 = \\\\;-\\\\;9$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reflexive property of equality for real numbers states that $$a = a$$, for any real number a.<br>\r\nThe statement $$a = \\\\;-\\\\;8$$ simply states that the value of the variable a is $$\\\\;-\\\\;8$$. It is not based on the reflexive property of equality.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x = x$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reflexive property of equality for real numbers states that $$a = a$$, for any real number a.<br>\r\nThe statement $$a = \\\\;-\\\\;8$$ simply states that the value of the variable a is $$\\\\;-\\\\;8$$. It is not based on the reflexive property of equality.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a = \\\\;-\\\\;8$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Reflexive property of equality for real numbers states that $$a = a$$, for any real number a.<br>\r\nThe statement $$a = \\\\;-\\\\;8$$ simply states that the value of the variable a is $$\\\\;-\\\\;8$$. It is not based on the reflexive property of equality.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$0 = 0$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Reflexive property of equality for real numbers states that $$a = a$$, for any real number a.<br>\r\nThe statement $$a = \\\\;-\\\\;8$$ simply states that the value of the variable a is $$\\\\;-\\\\;8$$. It is not based on the reflexive property of equality.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Reflexive property of equality for real numbers states that $$a = a$$, for any real number a.<br>\r\nThe statement $$a = \\\\;-\\\\;8$$ simply states that the value of the variable a is $$\\\\;-\\\\;8$$. It is not based on the reflexive property of equality.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"For any real number r, the statement $$r = r$$ is based on the\",\n                    \"text\": \"For any real number r, the statement $$r = r$$ is based on the\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"By the reflexive property of equality, every real number \u201cr\u201d is equal to itself.<br>\r\nIt can be denoted as$$ r = r$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Reflexive property of congruence\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the reflexive property of equality, every real number \u201cr\u201d is equal to itself.<br>\r\nIt can be denoted as$$ r = r$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Symmetric property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the reflexive property of equality, every real number \u201cr\u201d is equal to itself.<br>\r\nIt can be denoted as$$ r = r$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Transitive property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the reflexive property of equality, every real number \u201cr\u201d is equal to itself.<br>\r\nIt can be denoted as$$ r = r$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Reflexive property of equality\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"By the reflexive property of equality, every real number \u201cr\u201d is equal to itself.<br>\r\nIt can be denoted as$$ r = r$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"By the reflexive property of equality, every real number \u201cr\u201d is equal to itself.<br>\r\nIt can be denoted as$$ r = r$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following expressions is NOT based on the reflexive property of congruence?\",\n                    \"text\": \"Which of the following expressions is NOT based on the reflexive property of congruence?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"By the reflexive property of congruence, every geometric figure (an angle, line segment, or shape) is congruent to itself.<br>\r\n$$| (AB) = | (BA)$$ simply means that the length of the line segment remains the same. This is true regardless of the order of endpoints you choose to help name the segment. It is not based on the reflexive property of congruence.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\Delta ABC \\\\cong \\\\Delta ABC$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the reflexive property of congruence, every geometric figure (an angle, line segment, or shape) is congruent to itself.<br>\r\n$$| (AB) = | (BA)$$ simply means that the length of the line segment remains the same. This is true regardless of the order of endpoints you choose to help name the segment. It is not based on the reflexive property of congruence.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$XY \\\\cong XY$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the reflexive property of congruence, every geometric figure (an angle, line segment, or shape) is congruent to itself.<br>\r\n$$| (AB) = | (BA)$$ simply means that the length of the line segment remains the same. This is true regardless of the order of endpoints you choose to help name the segment. It is not based on the reflexive property of congruence.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle A \\\\cong \\\\angle A$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the reflexive property of congruence, every geometric figure (an angle, line segment, or shape) is congruent to itself.<br>\r\n$$| (AB) = | (BA)$$ simply means that the length of the line segment remains the same. This is true regardless of the order of endpoints you choose to help name the segment. It is not based on the reflexive property of congruence.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$| (AB) = | (BA)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"By the reflexive property of congruence, every geometric figure (an angle, line segment, or shape) is congruent to itself.<br>\r\n$$| (AB) = | (BA)$$ simply means that the length of the line segment remains the same. This is true regardless of the order of endpoints you choose to help name the segment. It is not based on the reflexive property of congruence.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"By the reflexive property of congruence, every geometric figure (an angle, line segment, or shape) is congruent to itself.<br>\r\n$$| (AB) = | (BA)$$ simply means that the length of the line segment remains the same. This is true regardless of the order of endpoints you choose to help name the segment. It is not based on the reflexive property of congruence.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-about-reflexive-property\">Frequently Asked Questions about Reflexive Property<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-1308cc7b-be9c-4c6e-af87-d1079cab6592\" 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-0-1308cc7b-be9c-4c6e-af87-d1079cab6592\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1308cc7b-be9c-4c6e-af87-d1079cab6592\"><strong>What is the equivalence 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-0-1308cc7b-be9c-4c6e-af87-d1079cab6592\">\n\n<p>A relation is an equivalence relation if it is reflexive, symmetric, and transitive.<\/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-1-1308cc7b-be9c-4c6e-af87-d1079cab6592\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1308cc7b-be9c-4c6e-af87-d1079cab6592\"><strong>Can the reflexive property be violated?<\/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-1-1308cc7b-be9c-4c6e-af87-d1079cab6592\">\n\n<p>Yes, the reflexive property is violated in some conditions. For instance, in certain non-classical logic, there is a possibility for an object to not have a relation to itself. This is called non-reflexivity.<\/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-2-1308cc7b-be9c-4c6e-af87-d1079cab6592\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1308cc7b-be9c-4c6e-af87-d1079cab6592\"><strong>Is the \u201cgreater than or equal to\u201d relation reflexive on the set of real numbers?<\/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-2-1308cc7b-be9c-4c6e-af87-d1079cab6592\">\n\n<p>Yes, the \u201cgreater than or equal to\u201d relation is reflexive since each real number is always equal to itself. For any real number x, we have $x \\ge x$.<\/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-3-1308cc7b-be9c-4c6e-af87-d1079cab6592\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1308cc7b-be9c-4c6e-af87-d1079cab6592\"><strong>What is the transitive property of equality?<\/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-3-1308cc7b-be9c-4c6e-af87-d1079cab6592\">\n\n<p>The transitive property states that for all real numbers a, b, and c<\/p>\n\n\n\n<p>if $a = b$ and $b = c$, then $a = c$.<\/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-4-1308cc7b-be9c-4c6e-af87-d1079cab6592\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1308cc7b-be9c-4c6e-af87-d1079cab6592\"><strong>What is a binary 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-4-1308cc7b-be9c-4c6e-af87-d1079cab6592\">\n\n<p>A binary relation R between sets A and B is a subset of the cartesian product $A \\times B$. It is a new set of ordered pairs (a, b) consisting of elements a in A and b in B.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Reflexive Property? Reflexive property is a fundamental property of relations which states that every element of a set is related to itself by that relation. Mathematically, a relation R on a set A is said to be reflexive if for all a \u2208 A, (a, a) \u2208 R. You can think of the &#8230; <a title=\"Reflexive Property &#8211; Definition, Equality, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/reflexiv-property\" aria-label=\"More on Reflexive Property &#8211; Definition, Equality, 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-30842","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\/30842","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=30842"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30842\/revisions"}],"predecessor-version":[{"id":36006,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30842\/revisions\/36006"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=30842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=30842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=30842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}