{"id":8353,"date":"2024-08-17T09:58:19","date_gmt":"2024-08-17T04:28:19","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=8353"},"modified":"2024-08-22T10:15:12","modified_gmt":"2024-08-22T04:45:12","slug":"ncert-solutions-class-11-maths-chapter-1-set-ex-1-5","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-5\/","title":{"rendered":"NCERT Solutions Class 11 Maths Chapter 1 Set \u2013 Ex 1.5"},"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 1.5 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-1-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 11 Maths Solution Ex &#8211; 1.2<\/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-1-3\/\" 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-1-6\/\" 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; 1.5<\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt; text-align: justify;\">1. Let U = {1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find<\/strong><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(i) A\u2019<br \/>\nSolution &#8211; <\/strong>We know that this is the complement of set A i.e, it is the subset of U. <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So,<strong>\u00a0A\u2019 = {5, 6, 7, 8, 9}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(ii) B\u2019<br \/>\nSolution &#8211;\u00a0<\/strong>We know that this is the complement of set B i.e, it is the subset of U. <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So,\u00a0<strong>B\u2019 = {1, 3, 5, 7, 9}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iii) (A <\/strong><strong>\u222a <\/strong><strong>C)\u2019<br \/>\nSolution &#8211;\u00a0<\/strong>This is the complement of union of set A and set C i.e, U \u2013 (A\u222a C) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So, A \u222a C = {1, 2, 3, 4, 5, 6} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 U \u2013 (A \u222a C) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So, (<strong>A \u222a C)\u2019 = {7, 8, 9}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iv) (A \u222a B)\u2019<br \/>\nSolution &#8211;\u00a0<\/strong>This is complement of union of set A and set B i.e, U- (A \u222a B) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So, A\u222a B = {1, 2, 3, 4, 6, 8} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 U \u2013 (A \u222a B) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So,\u00a0<strong>(A \u222a B)\u2019 = {5, 7, 9}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(v) (A\u2019)\u2019<br \/>\nSolution &#8211; <\/strong>This is the complement of set A i.e, (A\u2019)\u2019 = A <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So,\u00a0<strong>(A\u2019)\u2019 = {1, 2, 3, 4}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(vi) (B \u2013 C)\u2019<br \/>\nSolution &#8211;\u00a0 <\/strong>(B \u2013 C) = elements in B but not in C <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">(B \u2013 C) = {2, 8} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 U \u2013 (B \u2013 C) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">So,\u00a0<strong>(B \u2013 C)\u2019 = {1, 3, 4, 5, 6, 7, 9}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>2. If U = {<em>a, b, c, d, e, f, g, h<\/em>}, find the complements of the following sets:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(i)\u00a0A = {<em>a, b, c<\/em>}<br \/>\nSolution &#8211;<\/strong><br \/>\nComplement of set A = A\u2019 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">A\u2019 = U \u2013 A <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">A\u2019 = {a, b, c, d, e, f, g, h} \u2013 {a, b, c} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>A\u2019 = {d, e, f, g, h}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(ii)\u00a0B = {<em>d, e, f, g<\/em>}<br \/>\nSolution &#8211; <\/strong>Complement of set B = B\u2019 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">B\u2019 = U \u2013 B <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">B\u2019 = {a, b, c, d, e, f, g, h} \u2013 {d, e, f, g} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>B\u2019 = {a, b, c, h}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iii)\u00a0C = {<em>a, c, e, g<\/em>}<br \/>\nSolution &#8211;\u00a0<\/strong>Complement of set C = C\u2019<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">C\u2019 = U \u2013 C<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">C\u2019 = {a, b, c, d, e, f, g, h} \u2013 {a, c, e, g} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>C\u2019 = {b, d, f, h}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iv)\u00a0D = {<em>f<\/em>,\u00a0<em>g<\/em>,\u00a0<em>h<\/em>,\u00a0<em>a<\/em>}<br \/>\nSolution &#8211;\u00a0 \u00a0<\/strong>Complement of set D = D\u2019 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">D\u2019 = U \u2013 D <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">D\u2019 = {a, b, c, d, e, f, g, h} \u2013 {f, g, h, a} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>D\u2019 = {b, c, d, e}<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>3. Taking the set of natural numbers as the universal set, write down the complements of the following sets: <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(i)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is an even natural number}<br \/>\n<strong>(ii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is an odd natural number}<br \/>\n<strong>(iii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a positive multiple of 3}<br \/>\n<strong>(iv)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a prime number}<br \/>\n<strong>(v)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a natural number divisible by 3 and 5}<br \/>\n<strong>(vi)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a perfect square}<br \/>\n<strong>(vii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is perfect cube}<br \/>\n<strong>(viii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0+ 5 = 8}<br \/>\n<strong>(ix)\u00a0<\/strong>{<em>x<\/em>: 2<em>x<\/em>\u00a0+ 5 = 9}<br \/>\n<strong>(x)<\/strong> {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2265 7}<br \/>\n<strong>(xi)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and 2<em>x<\/em> + 1 &gt; 10} <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>Solution &#8211; <\/strong>We know that U = N: Set of natural numbers<br \/>\n<strong>(i)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is an even natural number}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em> is an odd natural number}<br \/>\n<strong>(ii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is an odd natural number}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is an even natural number}<br \/>\n<strong>(iii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a positive multiple of 3}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and<em>\u00a0x<\/em>\u00a0is not a multiple of 3}<br \/>\n<strong>(iv)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a prime number}\u00b4 ={<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a positive composite number and<em>\u00a0x<\/em>\u00a0= 1}<br \/>\n<strong>(v)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a natural number divisible by 3 and 5}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em> is a natural number that is not divisible by 3 or 5}<br \/>\n<strong>(vi)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a perfect square}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and\u00a0<em>x\u00a0<\/em>is not a perfect square}<br \/>\n<strong>(vii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a perfect cube}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and\u00a0<em>x\u00a0<\/em>is not a perfect cube}<br \/>\n<strong>(viii)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0+ 5 = 8}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and\u00a0<em>x<\/em>\u00a0\u2260 3}<br \/>\n<strong>(ix)\u00a0<\/strong>{<em>x<\/em>: 2<em>x<\/em>\u00a0+ 5 = 9}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and\u00a0<em>x<\/em>\u00a0\u2260 2}<br \/>\n<strong>(x)<\/strong>\u00a0{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2265 7}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and\u00a0<em>x<\/em> &lt; 7}<br \/>\n<strong>(xi)\u00a0<\/strong>{<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and 2<em>x<\/em>\u00a0+ 1 &gt; 10}\u00b4 = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0\u2208 N and\u00a0<em>x\u00a0<\/em>\u2264 9\/2} <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>4. If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(i) (A U B)\u2019 = A\u2019 \u2229 B\u2019<br \/>\nSolution &#8211;<br \/>\n<\/strong>\u21d2 (A \u222a B)\u2019= U \u2013 (A \u222a B) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2, 3, 4, 5, 6, 7, 8}<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 (A \u222a B)\u2019 = {1, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">A\u2019 \u2229 B\u2019 = (U \u2013 A) \u2229 (U \u2013 B) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 {1, 3, 5, 7, 9} \u2229 {1, 4, 6, 8, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 A\u2019 \u2229 B\u2019 = {1, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">Hence, Verified!!! \u00a0(A \u222a B)\u2019 = A\u2019 \u2229 B\u2019<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(ii) (A \u2229 B)\u2019 = A\u2019 U B\u2019<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>\u21d2 (A \u2229 B)\u2019 = U \u2013 (A \u2229 B)<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 {1, 2, 3, 4, 5, 6, 7, 8, 9} \u2013 {2}<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 (A \u2229 B)\u2032 = {1, 3, 4, 5, 6, 7, 8, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">A\u2019 \u222a B\u2019= (U \u2013 A) \u222a (U \u2013 B) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 {1, 3, 5, 7, 9} \u222a {1, 4, 6, 8, 9}<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">\u21d2 A\u2032 \u222a B\u2032 = {1, 3, 4, 5, 6, 7, 8, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">Hence, Verified!!! \u00a0(A \u2229 B)\u2032 = A\u2032 \u222a B\u2032 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>5. Draw appropriate Venn diagram for each of the following:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(i) (A U B)\u2019<br \/>\nSolution &#8211;<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-8354\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2024\/08\/NCERT-Solution-Class-11-Maths-Ex1.5-Q5i.jpg\" alt=\"NCER Maths Class 11 Solutions\" width=\"183\" height=\"109\" \/> <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(ii) A\u2019 \u2229 B\u2019<br \/>\nSolution &#8211;<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-8356\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2024\/08\/NCERT-Solution-Class-11-Maths-Ex1.5-Q5iii.jpg\" alt=\"NCER Maths Class 11 Solutions\" width=\"180\" height=\"106\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iii) (A \u2229 B)\u2019<br \/>\nSolution &#8211;<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-8355\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2024\/08\/NCERT-Solution-Class-11-Maths-Ex1.5-Q5ii.jpg\" alt=\"NCER Maths Class 11 Solutions\" width=\"182\" height=\"111\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iv) A\u2019 U B\u2019<br \/>\nSolution &#8211;<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-8357\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2024\/08\/NCERT-Solution-Class-11-Maths-Ex1.5-Q5iv.jpg\" alt=\"NCER Maths Class 11 Solutions\" width=\"177\" height=\"106\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>6. Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60\u00b0, what is A\u2019?<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>U = set of all triangles in plane <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">A = set of all triangles with at least one angle different from 60\u00b0 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\">A\u2019 = set of all triangles with no angle different from 60\u00b0 i.e, set of all triangles with all angles 60\u00b0 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>A\u2019 is the set of all equilateral triangle.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>7. Fill in the blanks to make each of the following a true statement:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(i)<\/strong> A U A\u2019 = ________<br \/>\n<strong>(ii)<\/strong> \u03a6\u2032 \u2229 A = ________<br \/>\n<strong>(iii)<\/strong> A \u2229 A\u2019 = ________<br \/>\n<strong>(iv)<\/strong> U\u2019 \u2229 A = ________ <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>Solution &#8211;\u00a0 \u00a0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(i)<\/strong> A \u222a A\u2032 = <span style=\"text-decoration: underline;\">U\u00a0<\/span><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(ii)<\/strong>\u00a0\u2205\u2032 \u2229 A = <span style=\"text-decoration: underline;\">A<\/span><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iii)<\/strong> A \u2229 A\u2032 = <span style=\"text-decoration: underline;\">\u2205<\/span><\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif; font-size: 12pt;\"><strong>(iv)<\/strong> U\u2032 \u2229 A = <span style=\"text-decoration: underline;\">\u2205<\/span><\/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 1.5 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":[1675,1679,1676,1685,1678,1680,1681],"class_list":["post-8353","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-1-5-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 v27.4) - 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