{"id":1816,"date":"2026-05-21T04:38:00","date_gmt":"2026-05-21T04:38:00","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1816"},"modified":"2026-06-19T15:35:15","modified_gmt":"2026-06-19T10:05:15","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":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-2047604742\"><div id=\"mymoc-3241284100\"><a href=\"https:\/\/amzn.to\/43YYZi3\" aria-label=\"smart-phones\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-300x76.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-1024x259.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-768x194.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"329\"><\/a><\/div><\/div><div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1816?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">14<\/span><\/div>\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 &ndash; 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) &isin; R for every a &isin; 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) &isin; R &rArr; (b, a) &isin; 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) &isin; R and (b, c) &isin; R &rArr; (a, c) &isin; 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, &hellip;, 14} defined by:<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(x, y) : 3x &minus; y = 0}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-612-683x1024.png\" alt=\"\" class=\"wp-image-4863\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-612-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-612-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-612-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-612-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-612.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(ii) Relation R in the set N of natural numbers defined as<\/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<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-611-819x1024.png\" alt=\"\" class=\"wp-image-4862\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-611-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-611-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-611-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-611.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as<\/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<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-613-683x1024.png\" alt=\"\" class=\"wp-image-4867\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-613-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-613-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-613-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-613-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-613.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iv) Relation R in the set Z of all integers defined as<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>R = {(x, y) : x &minus; y is an integer}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-615-819x1024.png\" alt=\"\" class=\"wp-image-4875\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-615-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-615-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-615-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-615.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">(v) Relation R in the set A of human beings in a town at a particular time given by<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(a) R = {(x, y) : x and y work at the same place}<br>(b) R = {(x, y) : x and y live in the same locality}<br>(c) R = {(x, y) : x is exactly 7 cm taller than y}<br>(d) R = {(x, y) : x is wife of y}<br>(e) R = {(x, y) : x is father of y}<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-614-683x1024.png\" alt=\"\" class=\"wp-image-4872\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-614-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-614-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-614-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-614-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-614.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\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 the relation R in the set R of real numbers, defined as<br>R = {(a, b) : a &le; b2} is neither reflexive nor symmetric nor transitive.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-616-683x1024.png\" alt=\"\" class=\"wp-image-4878\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-616-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-616-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-616-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-616-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-616.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\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\">Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"725\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-618-725x1024.png\" alt=\"\" class=\"wp-image-4885\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-618-725x1024.png 725w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-618-212x300.png 212w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-618-768x1085.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-618.png 1055w\" sizes=\"(max-width: 725px) 100vw, 725px\"><\/figure>\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 the relation R in R defined as R = {(a, b) : a &le; b}, is reflexive and transitive but not symmetric.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-617-819x1024.png\" alt=\"\" class=\"wp-image-4881\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-617-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-617-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-617-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-617.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\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 whether the relation R in R defined by R = {(a, b) : a &le; b3} is reflexive,<br>symmetric or transitive.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-619-819x1024.png\" alt=\"\" class=\"wp-image-4888\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-619-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-619-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-619-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-619.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is<br>symmetric but neither reflexive nor transitive.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Question 7<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Show that the relation R in the set A of all the books in a library of a college,<br>given by R = {(x, y) : x and y have same number of pages} is an equivalence<br>relation.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Question 8<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Show that the relation R in the set A = {1, 2, 3, 4, 5} given by<br>R = {(a, b) : |a &ndash; b| is even}, is an equivalence relation. Show that all the<br>elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are<br>related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Question 9<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Show that each of the relation R in the set A = {x &isin; Z : 0 &le; x &le; 12}, given by<br>(i) R = {(a, b) : |a &ndash; b| is a multiple of 4}<br>(ii) R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/relations-and-functions-exercise-1-2-solutions-class-12\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Relations and Functions Exercise 1.2 Solutions Class 12<\/span><\/a><\/div><p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Question 10<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Give an example of a relation. Which is<br>(i) Symmetric but neither reflexive nor transitive.<br>(ii) Transitive but neither reflexive nor symmetric.<br>(iii) Reflexive and symmetric but not transitive.<br>(iv) Reflexive and transitive but not symmetric.<br>(v) Symmetric and transitive but not reflexive.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Question 11<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P &ne; (0, 0) is the circle passing through P with origin as centre.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\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<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/miscellaneous-exercise-solutions-class-12-relations-functions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Miscellaneous Exercise Solutions Class 12 Relations Functions<\/span><\/a><\/div><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) &isin; R implies (b,a) &isin; 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 &le; b<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">is:<\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/inverse-trigonometric-functions-miscellaneous-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Inverse Trigonometric Functions Miscellaneous Solutions<\/span><\/a><\/div><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) &isin; R for every a &isin; 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) &isin; R &rArr; (b,a) &isin; 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><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-2827299465\"><div id=\"mymoc-3895998962\"><a href=\"https:\/\/amzn.to\/4ehJfM4\" aria-label=\"students acessories\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories.png 1301w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-300x85.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-1024x290.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-768x218.png 768w\" sizes=\"(max-width: 1301px) 100vw, 1301px\" width=\"1080\" height=\"100\"><\/a><\/div><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code>(a,b) &isin; R and (b,c) &isin; 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) &isin; 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\">&#128216; Prepare Smarter with MyMockMate!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Chapter-wise NCERT Solutions<br>&#9989; Important MCQs &amp; Notes<br>&#9989; Online Mock Tests<br>&#9989; Instant Result &amp; Analysis<br>&#9989; 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<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1816?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">14<\/span><\/div><div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-4201753698\"><div id=\"mymoc-2365676462\"><a href=\"https:\/\/amzn.to\/4uMTpup\" aria-label=\"books\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/books.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/books.png 1301w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/books-300x56.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/books-1024x190.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/books-768x143.png 768w\" sizes=\"(max-width: 1301px) 100vw, 1301px\" width=\"1301\" height=\"242\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p> 14 Short Intro In this post, students can find complete step-by-step solutions for Class 12 Maths Chapter 1 Exercise 1.1 &ndash; Relations and Functions&#8230;<\/p>\n","protected":false},"author":1,"featured_media":1817,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":""},"categories":[7,8],"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","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"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/Relations-and-Functions-Exercise-1.1-Solutions-Class-12.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"_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":12,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1816\/revisions"}],"predecessor-version":[{"id":4890,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1816\/revisions\/4890"}],"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}]}}