{"id":1816,"date":"2026-05-21T04:38:00","date_gmt":"2026-05-21T04:38:00","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1816"},"modified":"2026-05-21T04:38:02","modified_gmt":"2026-05-21T04:38:02","slug":"relations-and-functions-exercise-1-1-solutions-class-12","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/relations-and-functions-exercise-1-1-solutions-class-12\/","title":{"rendered":"Relations and Functions Exercise 1.1 Solutions Class 12"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">In this post, students can find complete step-by-step solutions for Class 12 Maths Chapter 1 Exercise 1.1 \u2013 Relations and Functions based on the latest NCERT syllabus. This exercise covers reflexive, symmetric, transitive, and equivalence relations in a simple and exam-oriented format.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Item<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Board<\/td><td>NCERT \/ CBSE<\/td><\/tr><tr><td>Class<\/td><td>12<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Chapter<\/td><td>Relations and Functions<\/td><\/tr><tr><td>Exercise<\/td><td>1.1<\/td><\/tr><tr><td>Main Topics<\/td><td>Relations &amp; Equivalence Relations<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Reflexive Relation<\/li>\n\n\n\n<li>Symmetric Relation<\/li>\n\n\n\n<li>Transitive Relation<\/li>\n\n\n\n<li>Equivalence Relation<\/li>\n\n\n\n<li>Universal Relation<\/li>\n\n\n\n<li>Empty Relation<\/li>\n\n\n\n<li>Equivalence Classes<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The chapter explains different types of relations and equivalence relations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Reflexive Relation<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>(a, a) \u2208 R for every a \u2208 A<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Symmetric Relation<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>(a, b) \u2208 R \u21d2 (b, a) \u2208 R<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Transitive Relation<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>(a, b) \u2208 R and (b, c) \u2208 R \u21d2 (a, c) \u2208 R<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Equivalence Relation<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>A relation which is reflexive, symmetric and transitive.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-step Solutions<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Determine whether the following relations are reflexive, symmetric and transitive.<\/h2>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Relation R in A = {1, 2, 3, \u2026, 14} defined by:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(x, y) : 3x \u2212 y = 0}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>y = 3x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Checking reflexive:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For reflexive relation:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>3x \u2212 x = 0<br>\u21d2 2x = 0<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Not true for all x.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is not reflexive.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Checking symmetric:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>3x \u2212 y = 0<br>\u21d2 y = 3x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>3y \u2212 x \u2260 0<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">in general.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is not symmetric.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Checking transitive:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>y = 3x and z = 3y<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>z = 9x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">But relation requires:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>z = 3x<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Not true.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is not transitive.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii) Relation in N:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(x, y) : y = x + 5 and x &lt; 4}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Possible ordered pairs:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(1,6), (2,7), (3,8)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">No pair of form:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(x, x)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Not reflexive.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Also:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(1,6) \u2208 R but (6,1) \u2209 R<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Not symmetric.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">No chain exists for transitivity.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is not transitive.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii) Relation in A = {1,2,3,4,5,6}<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(x, y) : y is divisible by x}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Every number divides itself.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is reflexive.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">But:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>2 divides 4<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">while:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>4 does not divide 2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is not symmetric.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x divides y and y divides z<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x divides z<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is transitive.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iv) Relation in Z:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(x, y) : x \u2212 y is an integer}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Since x and y are integers:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x \u2212 y is always an integer<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence relation is:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Reflexive, symmetric and transitive.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is an equivalence relation.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(v) Relations among human beings<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(a) Work at same place<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Reflexive, symmetric and transitive<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence equivalence relation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(b) Live in same locality<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Reflexive, symmetric and transitive<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence equivalence relation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(c) x is exactly 7 cm taller than y<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Neither reflexive nor symmetric nor transitive<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(d) x is wife of y<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Neither reflexive nor transitive<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Not symmetric.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(e) x is father of y<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Neither reflexive nor symmetric nor transitive<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Show that relation:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(a,b) : a \u2264 b\u00b2}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">is neither reflexive nor symmetric nor transitive.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Reflexive:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For all a:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a \u2264 a\u00b2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">fails for:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a = 1\/2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence not reflexive.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Symmetric:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a = 2, b = 3<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>2 \u2264 9<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">true.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>3 \u2264 4<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">may fail for other values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence not symmetric.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Transitive also fails.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is neither reflexive nor symmetric nor transitive.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Relation in {1,2,3,4,5,6}<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(a,b): b = a + 1}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Pairs:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(1,2), (2,3), (3,4), (4,5), (5,6)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">No pair:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(a,a)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence not reflexive.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Also:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(1,2) \u2208 R but (2,1) \u2209 R<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence not symmetric.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Further:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(1,2), (2,3) \u2208 R<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">but:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(1,3) \u2209 R<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence not transitive.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Show that:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(a,b): a \u2264 b}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">is reflexive and transitive but not symmetric.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Since:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a \u2264 a<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">R is reflexive.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a \u2264 b and b \u2264 c<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a \u2264 c<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence transitive.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>2 \u2264 5<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">does not imply:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>5 \u2264 2<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Hence not symmetric.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Check relation:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(a,b): a \u2264 b\u00b3}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Reflexive:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a \u2264 a\u00b3<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">not always true.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence not reflexive.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Symmetric and transitive also fail.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>R is neither reflexive nor symmetric nor transitive.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Confusing symmetric with transitive relation<\/li>\n\n\n\n<li>Forgetting ordered pair direction<\/li>\n\n\n\n<li>Missing counterexamples<\/li>\n\n\n\n<li>Incorrectly assuming every relation is reflexive<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always test all three properties separately.<\/li>\n\n\n\n<li>Use counterexamples to disprove properties.<\/li>\n\n\n\n<li>Write proper mathematical statements.<\/li>\n\n\n\n<li>Learn definitions thoroughly.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A relation which is reflexive, symmetric and transitive is called:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Universal relation<br>B. Empty relation<br>C. Equivalence relation<br>D. Identity relation<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. Equivalence relation<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If (a,b) \u2208 R implies (b,a) \u2208 R, then relation is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Reflexive<br>B. Symmetric<br>C. Transitive<br>D. Universal<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B. Symmetric<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Relation:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>a \u2264 b<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Symmetric<br>B. Reflexive only<br>C. Reflexive and transitive<br>D. None<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. Reflexive and transitive<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">What is a reflexive relation?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A relation where:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(a,a) \u2208 R for every a \u2208 A<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">What is symmetric relation?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(a,b) \u2208 R \u21d2 (b,a) \u2208 R<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">What is transitive relation?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(a,b) \u2208 R and (b,c) \u2208 R<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(a,c) \u2208 R<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">What is equivalence relation?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A relation which is reflexive, symmetric and transitive.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">CTA (Call To Action)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udcd8 Prepare Smarter with MyMockMate!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Chapter-wise NCERT Solutions<br>\u2705 Important MCQs &amp; Notes<br>\u2705 Online Mock Tests<br>\u2705 Instant Result &amp; Analysis<br>\u2705 CBSE Board Preparation Support<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start learning now on <a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.mymockmate.com?utm_source=chatgpt.com\">MyMockMate<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p>Short Intro In this post, students can find complete step-by-step solutions for Class 12 Maths Chapter 1 Exercise<\/p>\n","protected":false},"author":1,"featured_media":1817,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_angie_page":false,"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"page_builder":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[7,8,99],"tags":[187,175,174,186,182,183,180,146,138,190,53,47,191,192,177,185,193,173,176,189,188,184,178,179,181],"class_list":["post-1816","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-12","category-maths","category-relations-and-functions","tag-cbse-board-maths-preparation","tag-cbse-class-12-maths","tag-class-12-maths","tag-class-12-maths-chapter-1-solutions","tag-empty-relation","tag-equivalence-classes","tag-equivalence-relation","tag-exercise-1-1-ncert-solutions","tag-exercise-1-1-solutions","tag-mathematical-relations","tag-ncert-maths-solutions","tag-ncert-solutions","tag-one-one-relation","tag-onto-relation","tag-reflexive-relation","tag-relation-and-function-questions-answers","tag-relation-properties","tag-relations-and-functions","tag-relations-and-functions-chapter-1","tag-relations-and-functions-important-questions","tag-relations-and-functions-mcqs","tag-relations-and-functions-notes","tag-symmetric-relation","tag-transitive-relation","tag-universal-relation"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1816","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=1816"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1816\/revisions"}],"predecessor-version":[{"id":1818,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1816\/revisions\/1818"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1817"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}