{"id":1918,"date":"2026-05-22T12:44:38","date_gmt":"2026-05-22T12:44:38","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1918"},"modified":"2026-05-22T12:44:41","modified_gmt":"2026-05-22T12:44:41","slug":"miscellaneous-exercise-chapter-1-sets-solutions-class-11","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/miscellaneous-exercise-chapter-1-sets-solutions-class-11\/","title":{"rendered":"Miscellaneous Exercise Chapter 1 Sets Solutions Class 11"},"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\">This article provides complete NCERT Solutions for Miscellaneous Exercise of Chapter 1 \u2013 Sets for Class 11 Mathematics. Students will learn important concepts such as sets, subsets, union, intersection, complement, intervals and Venn diagrams with easy step-by-step explanations. These solutions are highly useful for CBSE Board Exams and competitive exam preparation.<\/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>Particular<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Class<\/td><td>11<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Chapter<\/td><td>Sets<\/td><\/tr><tr><td>Exercise<\/td><td>Miscellaneous Exercise<\/td><\/tr><tr><td>Board<\/td><td>NCERT \/ CBSE<\/td><\/tr><tr><td>Main Topics<\/td><td>Set Operations &amp; Venn Diagrams<\/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>Representation of Sets<\/li>\n\n\n\n<li>Empty Set<\/li>\n\n\n\n<li>Finite &amp; Infinite Sets<\/li>\n\n\n\n<li>Equal Sets<\/li>\n\n\n\n<li>Subsets<\/li>\n\n\n\n<li>Proper Subsets<\/li>\n\n\n\n<li>Universal Set<\/li>\n\n\n\n<li>Intervals<\/li>\n\n\n\n<li>Union &amp; Intersection<\/li>\n\n\n\n<li>Difference of Sets<\/li>\n\n\n\n<li>Complement of Sets<\/li>\n\n\n\n<li>Venn Diagrams<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The chapter introduces the fundamental theory of sets and their operations used in mathematics.<\/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\">Union of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>\u222a<\/mo><mi>B<\/mi><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mi>x<\/mi><mo>\u2208<\/mo><mi>A<\/mi><mtext>&nbsp;or&nbsp;<\/mtext><mi>x<\/mi><mo>\u2208<\/mo><mi>B<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">A\\cup B=\\{x:x\\in A\\text{ or }x\\in B\\}<\/annotation><\/semantics><\/math>A\u222aB={x:x\u2208A&nbsp;or&nbsp;x\u2208B}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Intersection of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mi>x<\/mi><mo>\u2208<\/mo><mi>A<\/mi><mtext>&nbsp;and&nbsp;<\/mtext><mi>x<\/mi><mo>\u2208<\/mo><mi>B<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">A\\cap B=\\{x:x\\in A\\text{ and }x\\in B\\}<\/annotation><\/semantics><\/math>A\u2229B={x:x\u2208A&nbsp;and&nbsp;x\u2208B}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Difference of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>\u2212<\/mo><mi>B<\/mi><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mi>x<\/mi><mo>\u2208<\/mo><mi>A<\/mi><mtext>&nbsp;and&nbsp;<\/mtext><mi>x<\/mi><mo mathvariant=\"normal\">\u2209<\/mo><mi>B<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">A-B=\\{x:x\\in A\\text{ and }x\\notin B\\}<\/annotation><\/semantics><\/math>A\u2212B={x:x\u2208A&nbsp;and&nbsp;x\u2208\/B}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Complement of Sets<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>A<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><mi>U<\/mi><mo>\u2212<\/mo><mi>A<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A&#8217;=U-A<\/annotation><\/semantics><\/math>A\u2032=U\u2212A<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">De Morgan\u2019s Laws<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u222a<\/mo><mi>B<\/mi><msup><mo stretchy=\"false\">)<\/mo><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><msup><mi>A<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>\u2229<\/mo><msup><mi>B<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(A\\cup B)&#8217;=A&#8217;\\cap B&#8217;<\/annotation><\/semantics><\/math>(A\u222aB)\u2032=A\u2032\u2229B\u2032<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><msup><mo stretchy=\"false\">)<\/mo><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><msup><mi>A<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>\u222a<\/mo><msup><mi>B<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(A\\cap B)&#8217;=A&#8217;\\cup B&#8217;<\/annotation><\/semantics><\/math>(A\u2229B)\u2032=A\u2032\u222aB\u2032<\/p>\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<p class=\"wp-block-paragraph\">Write the following sets in roster form.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mi>x<\/mi><mtext>&nbsp;is&nbsp;an&nbsp;integer&nbsp;and&nbsp;<\/mtext><mo>\u2212<\/mo><mn>3<\/mn><mo>\u2264<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mn>7<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">A=\\{x:x\\text{ is an integer and }-3\\le x&lt;7\\}<\/annotation><\/semantics><\/math>A={x:x&nbsp;is&nbsp;an&nbsp;integer&nbsp;and&nbsp;\u22123\u2264x&lt;7}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {\u22123, \u22122, \u22121, 0, 1, 2, 3, 4, 5, 6}<\/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)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mi>x<\/mi><mtext>&nbsp;is&nbsp;a&nbsp;natural&nbsp;number&nbsp;less&nbsp;than&nbsp;<\/mtext><mn>6<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">B=\\{x:x\\text{ is a natural number less than }6\\}<\/annotation><\/semantics><\/math>B={x:x&nbsp;is&nbsp;a&nbsp;natural&nbsp;number&nbsp;less&nbsp;than&nbsp;6}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>B = {1,2,3,4,5}<\/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)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Two-digit natural numbers whose digit sum is 8.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>C = {17,26,35,44,53,62,71,80}<\/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)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Prime divisors of 60.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>D = {2,3,5}<\/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<p class=\"wp-block-paragraph\">Find whether the following are finite or infinite sets.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Set of months in a year.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Finite Set<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">because it contains 12 elements.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Set of natural numbers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Infinite Set<\/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)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Set of points on a line.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Infinite Set<\/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<p class=\"wp-block-paragraph\">Determine equal sets.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {1,2,3}<br>B = {3,2,1}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Both contain same elements.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A = B<\/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)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {a,b,c}<br>B = {a,b,c,d}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>A \u2260 B<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">because B has an extra element d.<\/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<p class=\"wp-block-paragraph\">Find subsets of the following sets.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {a}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c6 , {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\">(ii)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>B = {a,b}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c6 , {a}, {b}, {a,b}<\/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)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>C = {1,2,3}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c6, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}<\/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 5<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Write intervals in set-builder form.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>(\u22123,0)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mo>\u2212<\/mo><mn>3<\/mn><mo>&lt;<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mn>0<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:-3&lt;x&lt;0\\}<\/annotation><\/semantics><\/math>{x:\u22123&lt;x&lt;0}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;6,12]<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mn>6<\/mn><mo>\u2264<\/mo><mi>x<\/mi><mo>\u2264<\/mo><mn>12<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:6\\le x\\le12\\}<\/annotation><\/semantics><\/math>{x:6\u2264x\u226412}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii)<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>(6,12]<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mn>6<\/mn><mo>&lt;<\/mo><mi>x<\/mi><mo>\u2264<\/mo><mn>12<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:6&lt;x\\le12\\}<\/annotation><\/semantics><\/math>{x:6&lt;x\u226412}<\/p>\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<p class=\"wp-block-paragraph\">Find union and intersection.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {1,2,3,4}<br>B = {3,4,5,6}<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Union<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>\u222a<\/mo><mi>B<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A\\cup B<\/annotation><\/semantics><\/math>A\u222aB<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>A \u222a B = {1,2,3,4,5,6}<\/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) Intersection<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A\\cap B<\/annotation><\/semantics><\/math>A\u2229B<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>A \u2229 B = {3,4}<\/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 7<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find difference of sets.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {1,2,3,4,5}<br>B = {2,4}<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>\u2212<\/mo><mi>B<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A-B<\/annotation><\/semantics><\/math>A\u2212B<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>A \u2212 B = {1,3,5}<\/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)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>B<\/mi><mo>\u2212<\/mo><mi>A<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">B-A<\/annotation><\/semantics><\/math>B\u2212A<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>B \u2212 A = \u03c6<\/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 8<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find complement of set.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>U = {1,2,3,4,5,6,7,8}<br>A = {2,4,6,8}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>A<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><mi>U<\/mi><mo>\u2212<\/mo><mi>A<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A&#8217;=U-A<\/annotation><\/semantics><\/math>A\u2032=U\u2212A<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A\u2032 = {1,3,5,7}<\/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 \u2208 and \u2282<\/li>\n\n\n\n<li>Repeating elements in sets<\/li>\n\n\n\n<li>Incorrect interval notation<\/li>\n\n\n\n<li>Mixing union and intersection symbols<\/li>\n\n\n\n<li>Forgetting complement is taken with respect to universal set<\/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>Learn all set symbols carefully.<\/li>\n\n\n\n<li>Practice Venn diagrams regularly.<\/li>\n\n\n\n<li>Remember:<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>A \u222a \u03c6 = A<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">and<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A \u2229 \u03c6 = \u03c6<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use step-by-step method in board exams.<\/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\">Which set is subset of every set?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Universal Set<br>B. Empty Set<br>C. Singleton Set<br>D. Infinite Set<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>B. Empty Set<\/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:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {1,2}<br>B = {2,3}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">then:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A\\cap B<\/annotation><\/semantics><\/math>A\u2229B<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">equals:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. {1}<br>B. {2}<br>C. {3}<br>D. \u03c6<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>B. {2}<\/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\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {1,2,3}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">then number of subsets is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. 4<br>B. 6<br>C. 8<br>D. 16<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>C. 8<\/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\">Q1. What is a set?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A well-defined collection of objects is called a set.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. What is empty set?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A set having no element is called empty set or null set.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. What is subset?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If every element of A belongs to B, then A is subset of B.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. What is complement of set?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Complement contains all elements of universal set which are not in the given set.<\/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 NCERT Solutions<br>\u2705 Chapter-wise Notes<br>\u2705 Important MCQs<br>\u2705 Online Mock Tests<br>\u2705 Instant Performance Analysis<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start your preparation today on <a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.mymockmate.com?utm_source=chatgpt.com\">MyMockMate<\/a><\/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 This article provides complete NCERT Solutions for Miscellaneous Exercise of Chapter 1 \u2013 Sets for Class<\/p>\n","protected":false},"author":1,"featured_media":1919,"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":[6,9,135],"tags":[187,286,285,301,329,338,298,292,290,304,291,297,320,306,62,342,206,308,159,47,318,300,311,309,307,287,303,294,296,295,299],"class_list":["post-1918","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-11","category-maths-class-11","category-sets","tag-cbse-board-maths-preparation","tag-cbse-class-11-maths","tag-class-11-maths","tag-class-11-maths-notes","tag-complement-of-sets","tag-de-morgan-laws","tag-difference-of-sets","tag-empty-set","tag-finite-sets","tag-important-questions-sets","tag-infinite-sets","tag-intersection-of-sets","tag-intervals","tag-mathematical-sets","tag-maths-chapter-1-solutions","tag-miscellaneous-exercise","tag-miscellaneous-exercise-solutions","tag-mymockmate","tag-ncert-maths-notes","tag-ncert-solutions","tag-proper-subsets","tag-set-operations","tag-set-theory","tag-sets","tag-sets-and-relations","tag-sets-chapter-1","tag-sets-mcqs","tag-subsets","tag-union-of-sets","tag-universal-set","tag-venn-diagram"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1918","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=1918"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1918\/revisions"}],"predecessor-version":[{"id":1920,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1918\/revisions\/1920"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1919"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}