CBSE Class 11 Maths Chapter Sets - NCERT Exercise 1.4 (Q 6 - Q 8) (#eduvictors)(#class11)

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)

Answer:
(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


Answer:
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}

Answer:
(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.


☞See also:
Special Mathematical Constants

 SETS (NCERT Ex 1.1)
 SETS (NCERT Ex 1.2)
 Different Types of Sets
 SETS (NCERT Ex 1.3)

 SETS (Unit Test Paper)
SETS (VENN DIAGRAMS)
SETS (Operations of Sets)
SETS (NCERT Ex 1.4 Q1-Q5)