NCERT Solutions Class 11th Maths Chapter – 1- Sets Exercise 1.5<\/span><\/strong><\/span><\/h3>\n

?Chapter – 1?<\/span><\/strong><\/span><\/p>\n

\u270d Sets \u270d<\/span><\/strong><\/span><\/p>\n

?Exercise 1.5?<\/span><\/strong><\/span><\/p>\n

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><\/span>
\n(i) A\u2019<\/strong><\/span>
\n(ii) B\u2019<\/strong><\/span>
\n(iii) (A U C)\u2019<\/strong><\/span>
\n(iv) (A U B)\u2019<\/strong><\/span>
\n(v) (A\u2019)\u2019<\/strong><\/span>
\n(vi) (B \u2013 C)\u2019<\/strong><\/span><\/p>\n

Solution:<\/span><\/span><\/strong> It is given that<\/span><\/span>
\nU = {1, 2, 3, 4, 5, 6, 7, 8, 9}<\/span>
\nA = {1, 2, 3, 4}<\/span>
\nB = {2, 4, 6, 8}<\/span>
\nC = {3, 4, 5, 6}<\/span><\/p>\n

(i) A\u2019 = {5, 6, 7, 8, 9}<\/strong><\/span><\/p>\n

(ii) B\u2019 = {1, 3, 5, 7, 9}<\/strong><\/span><\/p>\n

(iii) A U C = {1, 2, 3, 4, 5, 6}<\/strong><\/span>
\nSo we get<\/span>
\n(A U C)\u2019 = {7, 8, 9}<\/span><\/p>\n

(iv) A U B = {1, 2, 3, 4, 6, 8}<\/strong><\/span>
\nSo we get<\/span>
\n(A U B)\u2019 = {5, 7, 9}<\/span><\/p>\n

(v) (A\u2019)\u2019 = A = {1, 2, 3, 4}<\/strong><\/span><\/p>\n

(vi) B \u2013 C = {2, 8}<\/strong><\/span>
\nSo we get<\/span>
\n(B \u2013 C)\u2019 = {1, 3, 4, 5, 6, 7, 9}<\/span><\/p>\n

2. If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:<\/strong><\/span>
\n(i)\u00a0A = {a, b, c}<\/strong><\/span>
\n(ii)\u00a0B = {d, e, f, g}<\/strong><\/span>
\n(iii)\u00a0C = {a, c, e, g}<\/strong><\/span>
\n(iv)\u00a0D = {f,\u00a0g,\u00a0h,\u00a0a}<\/strong><\/span><\/p>\n

Solution:<\/span><\/span><\/strong><\/span>
\n(i)\u00a0A = {a, b, c}<\/strong><\/span>
\nSo we get<\/span>
\nA\u2019 = {d, e, f, g, h}<\/span><\/p>\n

(ii)\u00a0B = {d, e, f, g}<\/strong><\/span>
\nSo we get<\/span>
\nB\u2019 = {a, b, c, h}<\/span><\/p>\n

(iii)\u00a0C = {a, c, e, g}<\/strong><\/span>
\nSo we get<\/span>
\nC\u2019 = {b, d, f, h}<\/span><\/p>\n

(iv)\u00a0D = {f,\u00a0g,\u00a0h,\u00a0a}<\/strong><\/span>
\nSo we get<\/span>
\nD\u2019 = {b, c, d, e}<\/span><\/p>\n

3. Taking the set of natural numbers as the universal set, write down the complements of the following sets:<\/strong><\/span>
\n(i)\u00a0{x:\u00a0x\u00a0is an even natural number}<\/strong><\/span>
\n(ii)\u00a0{x:\u00a0x\u00a0is an odd natural number}<\/strong><\/span>
\n(iii)\u00a0{x:\u00a0x\u00a0is a positive multiple of 3}<\/strong><\/span>
\n(iv)\u00a0{x:\u00a0x\u00a0is a prime number}<\/strong><\/span>
\n(v)\u00a0{x:\u00a0x\u00a0is a natural number divisible by 3 and 5}<\/strong><\/span>
\n(vi)\u00a0{x:\u00a0x\u00a0is a perfect square}<\/strong><\/span>
\n(vii)\u00a0{x:\u00a0x\u00a0is perfect cube}<\/strong><\/span>
\n(viii)\u00a0{x:\u00a0x\u00a0+ 5 = 8}<\/strong><\/span>
\n(ix)\u00a0{x: 2x\u00a0+ 5 = 9}<\/strong><\/span>
\n(x)\u00a0{x:\u00a0x\u00a0\u2265 7}<\/strong><\/span>
\n(xi)\u00a0{x:\u00a0x\u00a0\u2208 N and 2x\u00a0+ 1 > 10}<\/strong><\/span><\/p>\n

Solution:<\/span><\/span><\/strong> We know that<\/span><\/span>
\nU = N: Set of natural numbers<\/span>
\n(i)\u00a0{x:\u00a0x\u00a0is an even natural number}\u00b4 = {x:\u00a0x\u00a0is an odd natural number}<\/span>
\n(ii)\u00a0{x:\u00a0x\u00a0is an odd natural number}\u00b4 = {x:\u00a0x\u00a0is an even natural number}<\/span>
\n(iii)\u00a0{x:\u00a0x\u00a0is a positive multiple of 3}\u00b4 = {x:\u00a0x\u00a0\u2208 N and\u00a0x\u00a0is not a multiple of 3}<\/span>
\n(iv)\u00a0{x:\u00a0x\u00a0is a prime number}\u00b4 ={x:\u00a0x\u00a0is a positive composite number and\u00a0x\u00a0= 1}<\/span>
\n(v)\u00a0{x:\u00a0x\u00a0is a natural number divisible by 3 and 5}\u00b4 = {x:\u00a0x\u00a0is a natural number that is not divisible by 3 or 5}<\/span>
\n(vi)\u00a0{x:\u00a0x\u00a0is a perfect square}\u00b4 = {x:\u00a0x\u00a0\u2208 N and\u00a0x\u00a0is not a perfect square}<\/span>
\n(vii)\u00a0{x:\u00a0x\u00a0is a perfect cube}\u00b4 = {x:\u00a0x\u00a0\u2208 N and\u00a0x\u00a0is not a perfect cube}<\/span>
\n(viii)\u00a0{x:\u00a0x\u00a0+ 5 = 8}\u00b4 = {x:\u00a0x\u00a0\u2208 N and\u00a0x\u00a0\u2260 3}<\/span>
\n(ix)\u00a0{x: 2x\u00a0+ 5 = 9}\u00b4 = {x:\u00a0x\u00a0\u2208 N and\u00a0x\u00a0\u2260 2}<\/span>
\n(x)\u00a0{x:\u00a0x\u00a0\u2265 7}\u00b4 = {x:\u00a0x\u00a0\u2208 N and\u00a0x\u00a0< 7}<\/span>
\n(xi)\u00a0{x:\u00a0x\u00a0\u2208 N and 2x\u00a0+ 1 > 10}\u00b4 = {x:\u00a0x\u00a0\u2208 N and\u00a0x\u00a0\u2264 9\/2}<\/span><\/p>\n

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>
\n(i) (A U B)\u2019 = A\u2019 \u2229 B\u2019<\/strong><\/span>
\n(ii) (A \u2229 B)\u2019 = A\u2019 U B\u2019<\/strong><\/span><\/p>\n

Solution:<\/span><\/span><\/strong> It is given that<\/span><\/span>
\nU = {1, 2, 3, 4, 5,6,7,8, 9}<\/span>
\nA = {2, 4, 6, 8}<\/span>
\nB = {2, 3, 5, 7}<\/span><\/p>\n

(i) (A U B)\u2019 = {2, 3, 4, 5, 6, 7, 8}\u2019 = {1, 9}<\/strong><\/span>
\nA\u2019 \u2229 B\u2019 = {1, 3, 5, 7, 9} \u2229 {1, 4, 6, 8, 9} = {1, 9}<\/span>
\nTherefore, (A U B)\u2019 = A\u2019 \u2229 B\u2019.<\/span><\/p>\n

(ii) (A \u2229 B)\u2019 = {2}\u2019 = {1, 3, 4, 5, 6, 7, 8, 9}<\/strong><\/span>
\nA\u2019 U B\u2019 = {1, 3, 5, 7, 9} U {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9}<\/span>
\nTherefore, (A \u2229 B)\u2019 = A\u2019 U B\u2019.<\/span><\/p>\n

5. Draw appropriate Venn diagram for each of the following:<\/strong><\/span>
\n(i) (A U B)\u2019<\/strong><\/span>
\n(ii) A\u2019 \u2229 B\u2019<\/strong><\/span>
\n(iii) (A \u2229 B)\u2019<\/strong><\/span>
\n(iv) A\u2019 U B\u2019<\/strong><\/span><\/p>\n

Solution:<\/span><\/span><\/strong><\/span><\/p>\n

(i) (A U B)\u2019<\/strong><\/span><\/p>\n

<\/span><\/p>\n

(ii) A\u2019 \u2229 B\u2019<\/strong><\/span><\/p>\n

<\/span><\/p>\n

(iii) (A \u2229 B)\u2019<\/strong><\/span><\/p>\n

<\/span><\/p>\n

(iv) A\u2019 U B\u2019<\/strong><\/span><\/p>\n

<\/span><\/p>\n

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?<\/strong><\/span><\/p>\n

Solution:<\/span><\/span> <\/strong>A\u2019 is the set of all equilateral triangles.<\/span><\/span><\/p>\n

7. Fill in the blanks to make each of the following a true statement:<\/strong><\/span>
\n(i) A U A\u2019 = \u2026\u2026..<\/strong><\/span>
\n(ii) \u03a6\u2032 \u2229 A = \u2026\u2026.<\/strong><\/span>
\n(iii) A \u2229 A\u2019 = \u2026\u2026.<\/strong><\/span>
\n(iv) U\u2019 \u2229 A = \u2026\u2026.<\/strong><\/span><\/p>\n

Solution:<\/span><\/span><\/strong><\/span>
\n(i) A U A\u2019 = U<\/strong><\/span><\/p>\n

(ii) \u03a6\u2032 \u2229 A = U \u2229 A = A<\/strong><\/span>
\nSo we get<\/span>
\n\u03a6\u2032 \u2229 A = A<\/span><\/p>\n

(iii) A \u2229 A\u2019 = \u03a6<\/strong><\/span><\/p>\n

(iv) U\u2019 \u2229 A = \u03a6 \u2229 A = \u03a6<\/strong><\/span>
\nSo we get<\/span>
\nU\u2019 \u2229 A = \u03a6<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

NCERT Solutions Class 11th Maths Chapter – 1- Sets Exercise 1.5 Textbook NCERT class Class – 11th Subject Mathematics Chapter Chapter – 1 Chapter Name Sets grade Class 11th Maths solution\u00a0 Medium\u00a0 English Source last doubt NCERT Solutions Class 11th Maths Chapter – 1- Sets Exercise 1.5 ?Chapter – 1? \u270d Sets \u270d ?Exercise 1.5? […]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[28],"tags":[11042,11078,11076,242,11041,11040,11038,11077,2249,3809],"class_list":{"0":"post-31472","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-last-doubt","7":"tag-class-11th-maths-english-medium-chapter-1","8":"tag-class-11th-maths-english-medium-chapter-1-sets-exercise-1-5","9":"tag-exercise-1-5","10":"tag-ncert","11":"tag-ncert-solutions-class-11th","12":"tag-ncert-solutions-class-11th-maths","13":"tag-ncert-solutions-class-11th-maths-chapter-1-sets","14":"tag-ncert-solutions-class-11th-maths-chapter-1-sets-exercise-1-5","15":"tag-social-science-civics","16":"tag---grammar"},"yoast_head":"\n