{"id":8346,"date":"2024-08-12T09:26:25","date_gmt":"2024-08-12T03:56:25","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=8346"},"modified":"2024-08-22T10:16:20","modified_gmt":"2024-08-22T04:46:20","slug":"ncert-solutions-class-11-maths-chapter-1-set-ex-1-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-2\/","title":{"rendered":"NCERT Solutions Class 11 Maths Chapter 1 Set \u2013 Ex 1.2"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">NCERT Solutions Class 11 Maths\u00a0<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 11 Mathematics <strong>Chapter &#8211; 1 Sets <\/strong>Exercise 1.2 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">Chapter 1 (Sets)\u00a0<\/span><\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\"><strong>Chapter : 1 Sets<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-1\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\">NCERT Class 11 Maths Solution Ex &#8211; 1.1<\/span><\/a><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 11 Maths Solution Ex &#8211; 1.3<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 11 Maths Solution Ex &#8211; 1.4<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-5\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 11 Maths Solution Ex &#8211; 1.5<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-6\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 11 Maths Solution Ex &#8211; 1.6<\/a><\/span><\/li>\n<\/ul>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; border-style: solid; border-color: #000000; background-color: #bddeab; text-align: center; height: 28px;\"><span style=\"font-family: georgia, palatino, serif; color: #ff0000; font-size: 14pt;\"><strong><span style=\"color: #000000;\">Exercise &#8211; 1.2<\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Which of the following are examples of the null set? <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) Set of odd natural numbers divisible by 2<br \/>\nSolution &#8211; <\/strong>Yes, this is a null set because three is no odd natural number divisible by 2.<br \/>\n<em><strong>Note &#8211;<\/strong> <\/em>A set which does not contain any element is called the null set.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) Set of even prime numbers<br \/>\nSolution &#8211; <\/strong>No, this is not a null set because 2 is an even number which is prime.\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) {<em>x<\/em>:\u00a0<em>x\u00a0<\/em>is a natural numbers,\u00a0<em>x\u00a0<\/em>&lt; 5 and\u00a0<em>x\u00a0<\/em>&gt; 7}<br \/>\nSolution &#8211;\u00a0<\/strong>Yes, this is a null set because three is no natural number which is less than 5 and greater than 7.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) {<em>y<\/em>:\u00a0<em>y\u00a0<\/em>is a point common to any two parallel lines}<br \/>\n<\/strong><strong>Solution &#8211; <\/strong>Yes, this is a null set because two parallel lines have no points in common because they do not intersect.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Which of the following sets are finite or infinite?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) The set of months of a year<br \/>\nSolution &#8211; <\/strong>This is a <strong>finite<\/strong> set because there is only 12 months in a year.\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) {1, 2, 3 \u2026}<br \/>\nSolution &#8211; <\/strong>This is an\u00a0<strong>infinite<\/strong>\u00a0set because there will always be a new number if we add 1 to the previous number, or we can say that it is a set of natural numbers and there are infinite natural numbers.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) {1, 2, 3 \u2026 99, 100}<br \/>\nSolution &#8211; <\/strong>This is a\u00a0<strong>finite<\/strong>\u00a0set because there is only 100 numbers in the set.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) The set of positive integers greater than 100<br \/>\nSolution &#8211; <\/strong>This is an\u00a0<strong>infinite<\/strong>\u00a0set because there are infinite positive integers greater than 100 which can be generated by adding 1 to the previous number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) The set of prime numbers less than 99<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong>This is a\u00a0<strong>finite<\/strong>\u00a0set because prime numbers which are less than 99 are finite.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. State whether each of the following set is finite or infinite:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) The set of lines which are parallel to the\u00a0<em>x<\/em>-axis<br \/>\nSolution &#8211;\u00a0<\/strong><strong>Infinite.\u00a0<\/strong>We can draw infinite parallel lines with respect to the x-axis.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) The set of letters in the English alphabet<br \/>\nSolution &#8211;\u00a0<\/strong><strong>Finite.\u00a0<\/strong>There are only 26 letters in the English alphabet.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) The set of numbers which are multiple of 5<br \/>\nSolution &#8211;\u00a0<\/strong><strong>Infinite.\u00a0<\/strong>There are infinite numbers which are multiple of 5 namely {5, 10, 15 &#8230;.. }<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) The set of animals living on the earth<br \/>\nSolution &#8211;\u00a0<\/strong><strong>Finite.\u00a0<\/strong>The animals Living on the earth can be counted they are not infinite.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) The set of circles passing through the origin (0, 0)<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong><strong>Infinite.<\/strong>\u00a0We can draw infinite number of circles passing through the origin with different radius.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. In the following, state whether A = B or not:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) A = {<em>a<\/em>,\u00a0<em>b<\/em>,\u00a0<em>c<\/em>,\u00a0<em>d<\/em>}; B = {<em>d<\/em>,\u00a0<em>c<\/em>,\u00a0<em>b<\/em>,\u00a0<em>a<\/em>}<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong><strong>Yes.\u00a0<\/strong>Every element of A is also an element of B and every element of B is also an element of A namely {a, b, c, d}.\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong><strong>No.\u00a0<\/strong>12 is an element that is present in A but not in B and similarly 18 is an element present in B not in A.\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) A = {2, 4, 6, 8, 10}; B = {<em>x<\/em>:\u00a0<em>x\u00a0<\/em>is positive even integer and\u00a0<em>x\u00a0<\/em>\u2264 10}<br \/>\nSolution &#8211;\u00a0<\/strong><strong>Yes.\u00a0<\/strong>If we define set B it can be written like this {2, 4, 6, 8, 10} and therefore every element of A is also an element of B and every element of B is also an element of A.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) A = {<em>x<\/em>:\u00a0<em>x\u00a0<\/em>is a multiple of 10}; B = {10, 15, 20, 25, 30 \u2026}<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong><strong>No.<\/strong>\u00a0If we define B we can clearly see that {-40, -30, -20, -10, 0}. All these numbers are also multiples of 10, and they are not in set B. Hence A \u2260 B.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Are the following pair of sets equal? Give reasons. <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) A = {2, 3}; B = {<em>x<\/em>:\u00a0<em>x\u00a0<\/em>is solution of\u00a0<em>x<\/em><sup>2<\/sup>\u00a0+ 5<em>x\u00a0<\/em>+ 6 = 0}<br \/>\n<\/strong><strong>Solution &#8211; <\/strong><strong>No.<br \/>\n<\/strong>By solving the equation x<sup>2\u00a0<\/sup>+ 5x + 6, <\/span><br \/>\n<span style=\"color: #000000;\">x<sup>2\u00a0<\/sup>+ 5x + 6 = 0 <\/span><br \/>\n<span style=\"color: #000000;\">x<sup>2\u00a0<\/sup>+ 2x + 3x + 6 = 0 <\/span><br \/>\n<span style=\"color: #000000;\">(x + 2)(x + 3) = 0 <\/span><br \/>\n<span style=\"color: #000000;\">x = -2, -3 <\/span><br \/>\n<span style=\"color: #000000;\">Now it is clear that B can be defined as {-2, -3}. <\/span><br \/>\n<span style=\"color: #000000;\">Now -2, -3 are not in A and also 2, 3 is not in set B. Hence A \u2260 B.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) A = {<em>x<\/em>:\u00a0<em>x\u00a0<\/em>is a letter in the word FOLLOW}; B = {<em>y<\/em>:\u00a0<em>y\u00a0<\/em>is a letter in the word WOLF}<br \/>\n<\/strong><strong>Solution &#8211; <\/strong><strong>Yes.<br \/>\n<\/strong>It is clear that A can be defined as {F, O, L, W} an if we define B, {F, O, L, W}. Now it is clear that every element of A is also an element of B and every element of B is also an element of A namely {W, O, L, F}.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. From the sets given below, select equal sets:<br \/>\n<\/strong><strong>A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2} <\/strong><strong>E = {\u20131, 1}, F = {0,\u00a0<em>a<\/em>}, G = {1, \u20131}, H = {0, 1}<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong><strong>B = D &amp; E = G.<br \/>\nNote:\u00a0<\/strong>Two sets A and B are said to be equal if they have exactly the same elements.\u00a0 \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>For A<\/strong>, 8\u2208 A, but 8\u2209 B,8\u2209 B,8\u2209 D,8\u2209 E, 8\u2209 F,8\u2209 G,8\u2209 H, <\/span><br \/>\n<span style=\"color: #000000;\">Hence, A is not equal to B, D, E, F, G, H. <\/span><br \/>\n<span style=\"color: #000000;\">Also, 2\u2208 A, but 2\u2209 C Hence A, \u2260 C. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>For B<\/strong>, 2\u2208 B, but 2\u2209 C,2\u2209 E,2\u2209 F,2\u2209 G, 2\u2209 H. <\/span><br \/>\n<span style=\"color: #000000;\">Hence, B is not equal to C, E, F, G, H. <\/span><br \/>\n<span style=\"color: #000000;\">Also, Every element of B can be found in D namely {1, 2, 3, 4} and vice-versa is also true. Hence\u00a0<strong>B = D. <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>For C<\/strong>, 14\u2208 C, but 14\u2209 D,14\u2209 E,14\u2209 F,14\u2209 G, 14\u2209 H. <\/span><br \/>\n<span style=\"color: #000000;\">Hence C is not equal to D, E, F, G, H.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>For D<\/strong>, 2\u2208 D, but 12\u2209 E,2\u2209 F,2\u2209 G, 2\u2209 H. <\/span><br \/>\n<span style=\"color: #000000;\">Hence D is not equal to E, F, G, H. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>For E<\/strong>, -1\u2208 E, but -1\u2209 F, -1\u2209 H. <\/span><br \/>\n<span style=\"color: #000000;\">Hence E is not equal to F, H. <\/span><br \/>\n<span style=\"color: #000000;\">Also, Every element of E can be found in G namely {-1, 1} and vice-versa is also true. Hence\u00a0<strong>E = G. <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>For F,<\/strong> 0\u2208 F, but 0\u2209 G, 0\u2209 H. <\/span><br \/>\n<span style=\"color: #000000;\">Hence F is not equal to G, H.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>For G<\/strong>, -1\u2208 G, but -1\u2209 H. <\/span><br \/>\n<span style=\"color: #000000;\">Hence G is not equal to H. <\/span><br \/>\n<span style=\"color: #000000;\">So, we can observe that only\u00a0<strong>B = D &amp; E = G.\u00a0<\/strong><\/span><\/p>\n<p><span style=\"color: #0000ff; font-family: georgia, palatino, serif;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths\/\" target=\"_blank\" rel=\"noopener\"><b><i>Go Back To Chapters<\/i><\/b><\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 11 Maths\u00a0 The NCERT Solutions in English Language for Class 11 Mathematics Chapter &#8211; 1 Sets Exercise 1.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 1 (Sets)\u00a0 Chapter : 1 Sets NCERT Class 11 Maths Solution Ex &#8211; 1.1 NCERT Class 11 Maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1674],"tags":[1675,1679,1676,1682,1678,1680,1681],"class_list":["post-8346","post","type-post","status-publish","format-standard","hentry","category-class-11-maths","tag-class-11-ncert-mathematics-solutions","tag-class-11-ncert-solutions","tag-ncert-class-11-mathematics-chapter-1-sets-solutions","tag-ncert-class-11-mathematics-exercise-1-2-solutions","tag-ncert-class-11-mathematics-solutions","tag-ncert-solutions-class-11-mathematics","tag-ncert-solutions-class-11-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - 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