## Class 11  Maths Chapter Sets - NCERT Exercise 1.4 (Q 6 - Q 8)

NCERT Solutions

Q6: If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
(i) A ∩ B
(ii) B ∩ C
(iii) A ∩ C ∩ D
(iv) A ∩ C
(v) B ∩ D
(vi) A ∩ (B ∪ C)
(vii) A ∩ D
(viii) A ∩ (B ∪ D)
(ix) ( A ∩ B ) ∩ ( B ∪ C )
(x) ( A ∪ D) ∩ ( B ∪ C)

(i) A ∩ B  = {7,9,11}

(ii) B ∩ C = {11, 13}

(iii) A ∩ C ∩ D = {A ∩ C} ∩ D  = {11} ∩ {15, 17} = φ

(iv) A ∩ C = {11}

(v) B ∩ D = {7, 9, 11, 13}  ∩ {15, 17} = φ

(vi) A ∩ (B ∪ C)
= {3, 5, 7, 9, 11}  ∩ ({7, 9, 11, 13} ∪ {11, 13, 15})
= {3, 5, 7, 9, 11}  ∩ {7, 9, 11, 13, 15}
= {7, 9, 11}

(vii) A ∩ D = φ

(viii) A ∩ (B ∪ D)
= {3, 5, 7, 9, 11}  ∩ ({7, 9, 11, 13} ∪ {15, 17})
= {3, 5, 7, 9, 11}  ∩ {7, 9, 11, 13, 15, 17}
= {7, 9, 11}

(ix) ( A ∩ B ) ∩ ( B ∪ C )
= ({3, 5, 7, 9, 11} ∩ {7, 9, 11, 13})  ∩  ({7, 9, 11, 13} ∪ {11, 13, 15})
= {7, 9 11} ∩ {7, 9, 11,13, 15}
= {7, 9, 11}

(x) ( A ∪ D) ∩ ( B ∪ C)
= ({3, 5, 7, 9, 11} ∪ {15, 17} ) ∩ ( {7, 9, 11, 13} ∪ {11, 13, 15})
= {3, 5, 7, 9, 11, 15, 17} ∩ {7, 9, 11, 13, 15}
= {7, 9, 11, 15}

Q7: If A = {x : x is a natural number }, B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find
(i) A ∩ B
(ii) A ∩ C
(iii) A ∩ D
(iv) B ∩ C
(v) B ∩ D
(vi) C ∩ D

A = {x : x is a natural number} = {1,2,3,4,5...}
B = {x : x is an even natural number} = {2,4,6,8...}
C = {x : x is an odd natural number} = {1,3,5,7,9...}
D = {x : x is a prime number } = {2,3,5,7...}

(i) A ∩ B = {2,4,6,8...} = {x : x is a even natural number} = B

(ii) A ∩ C = {1,3,5,7,...} = {x : x is an odd natural number} = C

(iii) A ∩ D = {2,3,5,7...} = {x : x is a prime number }

(iv) B ∩ C = φ

(v) B ∩ D = {2}

(vi) C ∩ D = {x : x is odd prime number}

Q8: Which of the following pairs of sets are disjoint
(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }
(ii) { a, e, i, o, u } and { c, d, e, f }
(iii) {x : x is an even integer } and {x : x is an odd integer}

(i)  {1,2,3,4}
{x : x isa natural number and 4 ≤ x ≤ 6} = {4,5,6}

Now, {1,2,3,4}  ∩ {4,5,6} = {4}
Therefore, this pair of sets is not disjoint.

(ii) { a, e, i, o, u } ∩ { c, d, e, f } = {e}
Therefore, this pair of sets is not disjoint.

(iii) {x : x is an even integer } ∩ {x : x is an odd integer} = φ
Therefore, this pair of sets is disjoint.