{"id":1909,"date":"2026-05-22T11:23:19","date_gmt":"2026-05-22T11:23:19","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1909"},"modified":"2026-05-22T11:23:38","modified_gmt":"2026-05-22T11:23:38","slug":"sets-exercise-1-3-solutions-class-11-maths-ncert","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/sets-exercise-1-3-solutions-class-11-maths-ncert\/","title":{"rendered":"Sets Exercise 1.3 Solutions Class 11 Maths NCERT"},"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 11 Maths Chapter 1 Exercise 1.3 \u2013 Sets based on the latest NCERT syllabus. This exercise covers subsets, proper subsets, universal sets, intervals, Venn diagrams, and set 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>11<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Chapter<\/td><td>Sets<\/td><\/tr><tr><td>Exercise<\/td><td>1.3<\/td><\/tr><tr><td>Main Topics<\/td><td>Subsets &amp; Intervals<\/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>Subsets<\/li>\n\n\n\n<li>Proper Subsets<\/li>\n\n\n\n<li>Universal Set<\/li>\n\n\n\n<li>Singleton Set<\/li>\n\n\n\n<li>Empty Set<\/li>\n\n\n\n<li>Intervals on Real Number Line<\/li>\n\n\n\n<li>Open &amp; Closed Intervals<\/li>\n\n\n\n<li>Set Relations<\/li>\n\n\n\n<li>Venn Diagrams<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The exercise mainly focuses on subsets and interval representation.<\/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\">Subset Definition<\/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>\u2282<\/mo><mi>B<\/mi><mtext>\u2005\u200a<\/mtext><mo>\u27fa<\/mo><mtext>\u2005\u200a<\/mtext><mi>x<\/mi><mo>\u2208<\/mo><mi>A<\/mi><mo>\u21d2<\/mo><mi>x<\/mi><mo>\u2208<\/mo><mi>B<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A\\subset B\\iff x\\in A\\Rightarrow x\\in B<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Open Interval<\/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 separator=\"true\">,<\/mo><mi>b<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mi>a<\/mi><mo>&lt;<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mi>b<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(a,b)=\\{x:a&lt;x&lt;b\\}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Closed Interval<\/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 separator=\"true\">,<\/mo><mi>b<\/mi><mo stretchy=\"false\">]<\/mo><mo>=<\/mo><mo stretchy=\"false\">{<\/mo><mi>x<\/mi><mo>:<\/mo><mi>a<\/mi><mo>\u2264<\/mo><mi>x<\/mi><mo>\u2264<\/mo><mi>b<\/mi><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">[a,b]=\\{x:a\\le x\\le b\\}<\/annotation><\/semantics><\/math><\/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 Set<\/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><\/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\">Fill in the symbols \u2282 or \u2284.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{2,3,4} \u2282 {1,2,3,4,5}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">because every element of first set belongs to second set.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{a,b,c} \u2284 {b,c,d}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">because a does not belong to second set.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Students of Class XI of your school:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u2282<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">students of your school.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Circles in a plane:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u2284<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">circles having radius 1 unit.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(v)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Triangles in a plane:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u2284<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">rectangles in the plane.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(vi)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Equilateral triangles:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u2282<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">triangles in the plane.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(vii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Even natural numbers:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u2282<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">integers.<\/p>\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\">State True or False.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{a,b} \u2284 {b,c,a}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Both a and b belong to second set.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>False<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{a,e} \u2282 vowels<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>True<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{1,2,3} \u2282 {1,3,5}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2 does not belong to second set.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>False<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{a} \u2282 {a,b,c}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>True<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(v)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{a} \u2208 {a,b,c}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">a is element, not {a}<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>False<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(vi)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Even natural numbers less than 6:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u2282<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">natural numbers dividing 36.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>True<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">because 2 and 4 divide 36.<\/p>\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\">Let:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A = {1,2,{3,4},5}<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Find incorrect statements.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{3,4} \u2282 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">3 and 4 are not individual elements of A.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Incorrect<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{3,4} \u2208 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Correct<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">because {3,4} itself is an element of A.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{{3,4}} \u2282 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Correct<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>1 \u2208 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Correct<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(v)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>1 \u2282 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">1 is not a set.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Incorrect<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(vi)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{1,2,5} \u2282 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Correct<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(vii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{1,2,5} \u2208 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Not an element of A.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Incorrect<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(viii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{1,2,3} \u2282 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">3 is not direct element of A.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Incorrect<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ix)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c6 \u2208 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Empty set is not element of A.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Incorrect<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(x)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c6 \u2282 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Empty set is subset of every set.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Correct<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(xi)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{\u03c6} \u2282 A<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u03c6 is not element of A.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Incorrect<\/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 4<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Write all subsets.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{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<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{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<h3 class=\"wp-block-heading\">(iii)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>{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<h3 class=\"wp-block-heading\">(iv)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03c6<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>\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 5<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Write as intervals.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/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><mi>x<\/mi><mo>\u2208<\/mo><mi>R<\/mi><mo separator=\"true\">,<\/mo><mo>\u2212<\/mo><mn>4<\/mn><mo>&lt;<\/mo><mi>x<\/mi><mo>\u2264<\/mo><mn>6<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:x\\in R,-4&lt;x\\le6\\}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>(\u22124,6]<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/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><mi>x<\/mi><mo>\u2208<\/mo><mi>R<\/mi><mo separator=\"true\">,<\/mo><mo>\u2212<\/mo><mn>12<\/mn><mo>&lt;<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mo>\u2212<\/mo><mn>10<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:x\\in R,-12&lt;x&lt;-10\\}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>(\u221212,\u221210)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii)<\/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><mi>x<\/mi><mo>\u2208<\/mo><mi>R<\/mi><mo separator=\"true\">,<\/mo><mn>0<\/mn><mo>\u2264<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mn>7<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:x\\in R,0\\le x&lt;7\\}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;0,7)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv)<\/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><mi>x<\/mi><mo>\u2208<\/mo><mi>R<\/mi><mo separator=\"true\">,<\/mo><mn>3<\/mn><mo>\u2264<\/mo><mi>x<\/mi><mo>\u2264<\/mo><mn>4<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:x\\in R,3\\le x\\le4\\}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;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 6<\/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<h3 class=\"wp-block-heading\">(i)<\/h3>\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<h3 class=\"wp-block-heading\">(ii)<\/h3>\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><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii)<\/h3>\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><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iv)<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;\u221223,5)<\/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>23<\/mn><mo>\u2264<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mn>5<\/mn><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\{x:-23\\le x&lt;5\\}<\/annotation><\/semantics><\/math><\/p>\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\">Universal set for right triangles and isosceles triangles.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>Universal set can be the set of all triangles.<\/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\">Select universal sets for A, B and C.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Valid universal sets:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(i) and (iii)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">because they contain all elements of A, B and C.<\/p>\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>Treating element as subset<\/li>\n\n\n\n<li>Wrong interval notation<\/li>\n\n\n\n<li>Forgetting empty set is subset of every set<\/li>\n\n\n\n<li>Writing incorrect subsets<\/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 interval symbols carefully.<\/li>\n\n\n\n<li>Practice subset questions daily.<\/li>\n\n\n\n<li>Remember:<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>Element \u2260 Subset<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use Venn diagrams for clarity.<\/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 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<p class=\"wp-block-paragraph\">Answer:<\/p>\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\">Which interval represents:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0<\/mn><mo>\u2264<\/mo><mi>x<\/mi><mo>&lt;<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0\\le x&lt;5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. (0,5)<br>B. [0,5]<br>C. [0,5)<br>D. (0,5]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. &#91;0,5)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">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}<\/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. 2<br>B. 3<br>C. 4<br>D. 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. 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\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">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\">What is proper subset?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A \u2282 B and A \u2260 B<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">then A is proper 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\">What is universal set?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The main set under consideration is called universal set.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">What is an interval?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A set of real numbers lying between two numbers.<\/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 Notes &amp; MCQs<br>\u2705 Online Mock Tests<br>\u2705 Instant Result &amp; Analysis<br>\u2705 CBSE Board Preparation<\/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    <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 11 Maths Chapter 1 Exercise<\/p>\n","protected":false},"author":1,"featured_media":1910,"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":[187,286,285,301,322,292,317,65,304,324,320,306,62,308,159,47,321,318,325,300,323,305,309,307,287,303,319,294,295,299],"class_list":["post-1909","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-closed-interval","tag-empty-set","tag-exercise-1-3-ncert-solutions","tag-exercise-1-3-solutions","tag-important-questions-sets","tag-interval-representation","tag-intervals","tag-mathematical-sets","tag-maths-chapter-1-solutions","tag-mymockmate","tag-ncert-maths-notes","tag-ncert-solutions","tag-open-interval","tag-proper-subsets","tag-real-number-line-intervals","tag-set-operations","tag-set-relations","tag-set-theory-basics","tag-sets","tag-sets-and-relations","tag-sets-chapter-1","tag-sets-mcqs","tag-singleton-set","tag-subsets","tag-universal-set","tag-venn-diagram"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1909","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=1909"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1909\/revisions"}],"predecessor-version":[{"id":1911,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1909\/revisions\/1911"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1910"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1909"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1909"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}