{"id":8351,"date":"2024-08-17T09:57:51","date_gmt":"2024-08-17T04:27:51","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=8351"},"modified":"2024-08-22T10:15:20","modified_gmt":"2024-08-22T04:45:20","slug":"ncert-solutions-class-11-maths-chapter-1-set-ex-1-4","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-1-set-ex-1-4\/","title":{"rendered":"NCERT Solutions Class 11 Maths Chapter 1 Set \u2013 Ex 1.4"},"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 1.4 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-1-5\/\" 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; 1.4<\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>1. Find the union of each of the following pairs of sets: <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) X = {1, 3, 5} Y = {1, 2, 3}<br \/>\nSolution &#8211;<br \/>\n<\/strong>X = {1, 3, 5} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Y = {1, 2, 3} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the union of the pairs of set can be written as X \u222a Y= {1, 2, 3, 5}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)\u00a0A = {<em>a<\/em>,\u00a0<em>e<\/em>,\u00a0<em>i<\/em>,\u00a0<em>o<\/em>,\u00a0<em>u<\/em>} B = {<em>a<\/em>,\u00a0<em>b<\/em>,\u00a0<em>c<\/em>}<br \/>\nSolution &#8211;<br \/>\n<\/strong>A = {a, e, i, o, u} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">B = {a, b, c} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the union of the pairs of set can be written as A \u222a B = {a, b, c, e, i, o, u}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)\u00a0A = {<em>x<\/em>:\u00a0<em>x<\/em> is a natural number and multiple of 3}<br \/>\n<\/strong><strong>B = {<em>x<\/em>:\u00a0<em>x<\/em> is a natural number less than 6}<br \/>\nSolution &#8211;<br \/>\n<\/strong>A = {x: x is a natural number and multiple of 3} = {3, 6, 9 \u2026} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5, 6} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the union of the pairs of set can be written as <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">A \u222a B = {1, 2, 4, 5, 3, 6, 9, 12 \u2026} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, A \u222a B = {x: x = 1, 2, 4, 5 or a multiple of 3}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv)\u00a0A = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a natural number and 1 &lt;<em>\u00a0x<\/em> \u2264\u00a06}<br \/>\n<\/strong><strong>B = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a natural number and 6 &lt;<em>\u00a0x<\/em> &lt; 10}<br \/>\nSolution &#8211;<br \/>\n<\/strong>A = {x: x is a natural number and 1 &lt; x \u2264 6} = {2, 3, 4, 5, 6} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">B = {x: x is a natural number and 6 &lt; x &lt; 10} = {7, 8, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the union of the pairs of set can be written as A \u222a B = {2, 3, 4, 5, 6, 7, 8, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, A \u222a B = {x : x \u2208 N and 1 &lt; x &lt; 10}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(v) A = {1, 2, 3}, B = \u03a6<br \/>\n<\/strong><strong>Solution &#8211; <\/strong>A = {1, 2, 3}, B = \u03a6 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the union of the pairs of set can be written as A \u222a B = {1, 2, 3}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>2. Let A = {<em>a<\/em>,\u00a0<em>b<\/em>}, B = {<em>a<\/em>,\u00a0<em>b<\/em>,\u00a0<em>c<\/em>}. Is A \u2282 B? What is A \u222a B?<br \/>\n<\/strong><strong>Solution &#8211;\u00a0 <\/strong>It is given that <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">A = {a, b} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">B = {a, b, c} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Yes, A \u2282 B <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the union of the pairs of set can be written as A \u222a B = {a, b, c} = B<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>3. If A and B are two sets such that A \u2282 B, then what is A \u222a B?<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong>If A and B are two sets such that A\u00a0\u2282\u00a0B, then A\u00a0\u222a\u00a0B = B.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>4. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find<br \/>\n<\/strong><strong>(i)<\/strong> A \u222a B<br \/>\n<strong>(ii)\u00a0<\/strong>A\u00a0\u222a\u00a0C<br \/>\n<strong>(iii)\u00a0<\/strong>B\u00a0\u222a\u00a0C<br \/>\n<strong>(iv)\u00a0<\/strong>B\u00a0\u222a\u00a0D<br \/>\n<strong>(v)\u00a0<\/strong>A\u00a0\u222a\u00a0B\u00a0\u222a\u00a0C<br \/>\n<strong>(vi)\u00a0<\/strong>A\u00a0\u222a\u00a0B\u00a0\u222a\u00a0D<br \/>\n<strong>(vii)\u00a0<\/strong>B \u222a C \u222a D\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;\u00a0 <\/strong>It is given that<br \/>\nA = {1, 2, 3, 4], B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)\u00a0<\/strong>A\u00a0\u222a\u00a0B = {1, 2, 3, 4, 5, 6}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)\u00a0<\/strong>A\u00a0\u222a\u00a0C = {1, 2, 3, 4, 5, 6, 7, 8}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)\u00a0<\/strong>B\u00a0\u222a\u00a0C = {3, 4, 5, 6, 7, 8}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv)\u00a0<\/strong>B\u00a0\u222a\u00a0D = {3, 4, 5, 6, 7, 8, 9, 10}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(v)\u00a0<\/strong>A\u00a0\u222a\u00a0B\u00a0\u222a\u00a0C = {1, 2, 3, 4, 5, 6, 7, 8}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vi)\u00a0<\/strong>A\u00a0\u222a\u00a0B\u00a0\u222a\u00a0D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vii)<\/strong> B \u222a C \u222a D = {3, 4, 5, 6, 7, 8, 9, 10}\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>5. Find the intersection of each pair of sets: <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)\u00a0X = {1, 3, 5} Y = {1, 2, 3}<br \/>\nSolution &#8211;<\/strong><br \/>\nX = {1, 3, 5}, <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Y = {1, 2, 3} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the intersection of the given set can be written as X \u2229 Y = {1, 3}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)\u00a0A = {<em>a<\/em>,\u00a0<em>e<\/em>,\u00a0<em>i<\/em>,\u00a0<em>o<\/em>,\u00a0<em>u<\/em>} B = {<em>a<\/em>,\u00a0<em>b<\/em>,\u00a0<em>c<\/em>}<br \/>\nSolution &#8211;<br \/>\n<\/strong>A = {a, e, i, o, u}<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">B = {a, b, c} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the intersection of the given set can be written as A \u2229 B = {a}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)\u00a0A = {<em>x<\/em>:\u00a0<em>x<\/em> is a natural number and multiple of 3}<br \/>\n<\/strong><strong>B = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a natural number less than 6}<br \/>\nSolution &#8211;<br \/>\n<\/strong>A = {x: x is a natural number and multiple of 3} = (3, 6, 9 \u2026} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">B = {x: x is a natural number less than 6} = {1, 2, 3, 4, 5} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the intersection of the given set can be written as A \u2229 B = {3}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv)\u00a0A = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a natural number and 1 &lt;<em>\u00a0x<\/em> \u2264\u00a06}<br \/>\n<\/strong><strong>B = {<em>x<\/em>:\u00a0<em>x<\/em>\u00a0is a natural number and 6 &lt;<em>\u00a0x<\/em>\u00a0&lt; 10}<br \/>\nSolution &#8211;<br \/>\n<\/strong>A = {x: x is a natural number and 1 &lt; x \u2264 6} = {2, 3, 4, 5, 6} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">B = {x: x is a natural number and 6 &lt; x &lt; 10} = {7, 8, 9} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the intersection of the given set can be written as A \u2229 B = \u03a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(v) A = {1, 2, 3}, B = \u03a6<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>A = {1, 2, 3}, B = \u03a6 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, the intersection of the given set can be written as A \u2229 B = \u03a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>6. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) A \u2229 B<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong>A \u2229 B = {7, 9, 11}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)\u00a0B\u00a0\u2229\u00a0C<br \/>\nSolution &#8211; <\/strong>B \u2229 C = {11, 13}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)\u00a0A\u00a0\u2229\u00a0C\u00a0\u2229\u00a0D<br \/>\nSolution &#8211;<br \/>\n<\/strong>A \u2229 C \u2229 D = {A \u2229 C} \u2229 D <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= {11} \u2229 {15, 17} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= \u03a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv)\u00a0A\u00a0\u2229\u00a0C<br \/>\nSolution &#8211; <\/strong>A \u2229 C = {11}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(v)\u00a0B\u00a0\u2229\u00a0D<br \/>\nSolution &#8211; <\/strong>B \u2229 D = \u03a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vi)\u00a0A\u00a0\u2229\u00a0(B\u00a0\u222a\u00a0C)<br \/>\nSolution &#8211; <\/strong>A \u2229 (B \u222a C) = (A \u2229 B) \u222a (A \u2229 C) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= {7, 9, 11} \u222a {11} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= {7, 9, 11}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vii)\u00a0A\u00a0\u2229\u00a0D<br \/>\nSolution &#8211; <\/strong>A \u2229 D = \u03a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(viii)\u00a0A\u00a0\u2229\u00a0(B\u00a0\u222a\u00a0D)<br \/>\nSolution &#8211; <\/strong>A \u2229 (B \u222a D) = (A \u2229 B) \u222a (A \u2229 D) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= {7, 9, 11} \u222a \u03a6\u00a0 \u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= {7, 9, 11}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ix)\u00a0(A\u00a0\u2229\u00a0B)\u00a0\u2229\u00a0(B\u00a0\u222a\u00a0C)<br \/>\nSolution &#8211; <\/strong>(A \u2229 B) \u2229 (B \u222a C) <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= {7, 9, 11} \u2229 {7, 9, 11, 13, 15} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">= {7, 9, 11}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(x) (A \u222a D) \u2229 (B \u222a C)<br \/>\n<\/strong><strong>Solution &#8211;\u00a0 <\/strong>(A\u00a0\u222a\u00a0D)\u00a0\u2229\u00a0(B\u00a0\u222a\u00a0C)<br \/>\n= {3, 5, 7, 9, 11, 15, 17) \u2229 {7, 9, 11, 13, 15}<br \/>\n= {7, 9, 11, 15} <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>7. If A = {<em>x<\/em>:<em>\u00a0x<\/em> is a natural number}, B ={<em>x<\/em>:<em>\u00a0x<\/em> is an even natural number}, <\/strong><strong>C = {<em>x<\/em>:<em>\u00a0x<\/em>\u00a0is an odd natural number} and D = {<em>x<\/em>:<em>\u00a0x\u00a0<\/em>is a prime number}, find<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) <\/strong>A \u2229 B<strong><br \/>\n<\/strong><strong>(ii)\u00a0<\/strong>A\u00a0\u2229\u00a0C<strong><br \/>\n<\/strong><strong>(iii)\u00a0<\/strong>A\u00a0\u2229\u00a0D<strong><br \/>\n<\/strong><strong>(iv)<\/strong>\u00a0B\u00a0\u2229\u00a0C<strong><br \/>\n<\/strong><strong>(v)\u00a0<\/strong>B\u00a0\u2229\u00a0D<strong><br \/>\n<\/strong><strong>(vi) <\/strong>C \u2229 D\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;\u00a0 \u00a0<\/strong>It can be written as<br \/>\nA = {<em>x<\/em>:<em>\u00a0x<\/em> is a natural number} = {1, 2, 3, 4, 5 \u2026}<br \/>\nB ={<em>x<\/em>:<em>\u00a0x<\/em> is an even natural number} = {2, 4, 6, 8 \u2026}<br \/>\nC = {<em>x<\/em>:<em>\u00a0x<\/em> is an odd natural number} = {1, 3, 5, 7, 9 \u2026}<br \/>\nD = {<em>x<\/em>:<em>\u00a0x\u00a0<\/em>is a prime number} = {2, 3, 5, 7 \u2026}\u00a0 <\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)\u00a0<\/strong>A\u00a0\u2229B = {<em>x<\/em>:<em>\u00a0x<\/em> is a even natural number} = B<br \/>\n<strong>(ii)\u00a0<\/strong>A\u00a0\u2229\u00a0C = {<em>x<\/em>:<em>\u00a0x<\/em> is an odd natural number} = C<br \/>\n<strong>(iii)\u00a0<\/strong>A\u00a0\u2229\u00a0D = {<em>x<\/em>:<em>\u00a0x\u00a0<\/em>is a prime number} = D<br \/>\n<strong>(iv)\u00a0<\/strong>B \u2229 C = \u03a6<br \/>\n<strong>(v)\u00a0<\/strong>B \u2229 D = {2}<br \/>\n<strong>(vi)\u00a0<\/strong>C\u00a0\u2229\u00a0D = {<em>x<\/em>:<em>\u00a0x<\/em>\u00a0is odd prime number}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>8. Which of the following pairs of sets are disjoint? <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)\u00a0{1, 2, 3, 4} and {<em>x<\/em>:<em>\u00a0x\u00a0<\/em>is a natural number and 4\u00a0\u2264\u00a0<em>x<\/em>\u00a0\u2264\u00a06}<br \/>\nSolution &#8211;<br \/>\n<\/strong>{1, 2, 3, 4} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">{x: x is a natural number and 4 \u2264 x \u2264 6} = {4, 5, 6} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, we get <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">{1, 2, 3, 4} \u2229 {4, 5, 6} = {4} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, this pair of sets is not disjoint.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)\u00a0{<em>a<\/em>,\u00a0<em>e<\/em>,\u00a0<em>i<\/em>,\u00a0<em>o<\/em>,\u00a0<em>u<\/em>}and {<em>c<\/em>,\u00a0<em>d<\/em>,\u00a0<em>e<\/em>,\u00a0<em>f<\/em>}<br \/>\nSolution &#8211;<br \/>\n<\/strong>{a, e, i, o, u} \u2229 (c, d, e, f} = {e} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, {a, e, i, o, u} and (c, d, e, f} are not disjoint.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)\u00a0{<em>x<\/em>:<em>\u00a0x<\/em>\u00a0is an even integer} and {<em>x: x<\/em> is an odd integer}<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>{x: x is an even integer} \u2229 {x: x is an odd integer} = \u03a6 <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, this pair of sets is disjoint.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>9. If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, <\/strong><strong>C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> A \u2013 B<br \/>\n<strong>(ii)<\/strong> A \u2013 C<br \/>\n<strong>(iii)\u00a0<\/strong>A \u2013 D<br \/>\n<strong>(iv)\u00a0<\/strong>B \u2013 A<br \/>\n<strong>(v)\u00a0<\/strong>C \u2013 A<br \/>\n<strong>(vi)\u00a0<\/strong>D \u2013 A<br \/>\n<strong>(vii)\u00a0<\/strong>B \u2013 C<br \/>\n<strong>(viii)\u00a0<\/strong>B \u2013 D<br \/>\n<strong>(ix)\u00a0<\/strong>C \u2013 B<br \/>\n<strong>(x)\u00a0<\/strong>D \u2013 B<br \/>\n<strong>(xi)\u00a0<\/strong>C \u2013 D<br \/>\n<strong>(xii)\u00a0<\/strong>D \u2013 C<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;\u00a0 <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> A \u2013 B = {3, 6, 9, 15, 18, 21}<br \/>\n<strong>(ii)<\/strong> A \u2013 C = {3, 9, 15, 18, 21}<br \/>\n<strong>(iii) <\/strong>A \u2013 D = {3, 6, 9, 12, 18, 21}<br \/>\n<strong>(iv) <\/strong>B \u2013 A = {4, 8, 16, 20}<br \/>\n<strong>(v) <\/strong>C \u2013 A = {2, 4, 8, 10, 14, 16}<br \/>\n<strong>(vi)\u00a0<\/strong>D \u2013 A = {5, 10, 20}<br \/>\n<strong>(vii)\u00a0<\/strong>B \u2013 C = {20}<br \/>\n<strong>(viii)\u00a0<\/strong>B \u2013 D = {4, 8, 12, 16}<br \/>\n<strong>(ix)\u00a0<\/strong>C \u2013 B = {2, 6, 10, 14}<br \/>\n<strong>(x)\u00a0<\/strong>D \u2013 B = {5, 10, 15}<br \/>\n<strong>(xi)\u00a0<\/strong>C \u2013 D = {2, 4, 6, 8, 12, 14, 16}<br \/>\n<strong>(xii)\u00a0<\/strong>D \u2013 C = {5, 15, 20}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>10. If X = {<em>a<\/em>,\u00a0<em>b<\/em>,\u00a0<em>c<\/em>,\u00a0<em>d<\/em>} and Y = {<em>f<\/em>,\u00a0<em>b<\/em>,\u00a0<em>d, g<\/em>}, find\u00a0 <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) X \u2013 Y<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong>X \u2013 Y = {<em>a<\/em>,\u00a0<em>c<\/em>}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)\u00a0Y \u2013 X<br \/>\nSolution &#8211; <\/strong>Y \u2013 X = {<em>f<\/em>,\u00a0 <em>g<\/em>}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii) X \u2229 Y<br \/>\n<\/strong><strong>Solution &#8211;\u00a0 <\/strong>X\u00a0\u2229\u00a0Y = {<em>b<\/em>,\u00a0<em>d<\/em>} <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>11. If R is the set of real numbers and Q is the set of rational numbers, then what is R \u2013 Q?<br \/>\n<\/strong><strong>Solution &#8211;\u00a0<\/strong>We know that<br \/>\nR \u2013 Set of real numbers<br \/>\nQ \u2013 Set of rational numbers<br \/>\nHence, R \u2013 Q is a set of irrational numbers. <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>12. State whether each of the following statement is true or false. Justify your answer.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)\u00a0{2, 3, 4, 5} and {3, 6} are disjoint sets.<br \/>\nSolution &#8211; (<\/strong><em><strong>False)<br \/>\n<\/strong><\/em>If 3 \u2208 {2, 3, 4, 5}, 3 \u2208 {3, 6} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, we get {2, 3, 4, 5} \u2229 {3, 6} = {3}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)\u00a0{<em>a<\/em>,\u00a0<em>e<\/em>,\u00a0<em>i<\/em>,\u00a0<em>o<\/em>,\u00a0<em>u<\/em>\u00a0} and {<em>a<\/em>,\u00a0<em>b<\/em>,\u00a0<em>c<\/em>,\u00a0<em>d<\/em>} are disjoint sets.<br \/>\nSolution &#8211; (<em>False)<\/em><br \/>\n<\/strong>If a \u2208 {a, e, i, o, u}, a \u2208 {a, b, c, d} <\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, we get {a, e, i, o, u} \u2229 {a, b, c, d} = {a}<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)\u00a0{2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.<br \/>\nSolution &#8211;\u00a0<\/strong><strong>(<\/strong><em><strong>True)<br \/>\n<\/strong><\/em>Here {2, 6, 10, 14}\u00a0\u2229\u00a0{3, 7, 11, 15} =\u00a0\u03a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.<br \/>\n<\/strong><strong>Solution &#8211; (<em>True)<br \/>\n<\/em><\/strong>Here {2, 6, 10}\u00a0\u2229\u00a0{3, 7, 11} =\u00a0\u03a6<\/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 1.4 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":[1675,1679,1676,1684,1678,1680,1681],"class_list":["post-8351","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-1-4-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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