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NCERT Exemplar Class 11 Maths Chapter 1 Sets Exercise Solutions Match the Following Question
Table of Contents
Solved Match the following Type Question of NCERT Exemplar Sets Exercise
Question 52. Match the following sets for all sets A, B and C:
List 1:
(i) ((A′ ∪ B′) – A)′
(ii) [B′ ∪ (B′ – A)]′
(iii) (A – B) – (B – C)
(iv) (A – B) ∩ (C – B)
(v) A × (B ∩ C)
(vi) A × (B ∪ C)
List 2:
(a) A – B
(b) A
(c) B
(d) (A × B) ∩ (A × C)
(e) (A × B) ∪ (A × C)
(f) (A ∩ C) – B
Answer 52
(i) ((A′ ∪ B′) – A)′ = [(A′ ∪ B′) ∩ A′]′ [ We know that A-B = A ∩ B′ ]
Using De Morgan’s Law : (A ∩ B)′ = A′ ∪ B′
[(A′ ∪ B′) ∩ A′]′ = (A′ ∪ B′)′ ∪ (A′)′ = (A ∩ B) ∪ A = A
(i) matches with (b)
(ii) [B′ ∪ (B′ – A)]′ = [B′ ∪ (B′ ∩ A′)]′ [ We know that A-B = A ∩ B′ ]
Using De Morgan’s Law : (A ∪ B)´ = A′ ∩ B′
[B′ ∪ (B′ ∩ A′)]′ = (B′)′ ∩ (B′ ∩ A′)′ = B ∩ (B ∪ A) = B
(ii) matches with (c)
(iii) (A – B) – (B – C) = (A ∩ B′) – (B ∩ C′) = (A ∩ B′) ∩ (B ∩ C′)′ = (A ∩ B′) ∩(B′ ∪ C) = [A ∩ (B′ ∪ C)] ∩ [ B′ ∩ (B′ ∪ C) ] = [A ∩ (B′ ∪ C)] ∩ B′
Using Associativity of Intersection
A ∩ [(B′ ∪ C) ∩ B′ ] = A ∩ B′ as intersection of B complement, union C, and then intersection with B complement will be B complement only
Further A ∩ B′ = A – B
(iii) matches with (a)
(iv) (A – B) ∩ (C – B) = (A ∩ B′) ∩ (C ∩ B′)
Since intersection is associative and commutative:
(A ∩ B′) ∩ (C ∩ B′) = (A ∩ B′) ∩ (B′∩ C) = [(A ∩ B′) ∩ B′] ∩ C = A ∩ B′ ∩ C = A ∩ C ∩ B′ = (A ∩ C) – B
(iv) matches with (f)
(v) A × (B ∩ C) = (A × B) ∩ (A × C)
(v) matches with (d)
(vi) A × (B ∪ C) = (A × B) ∪ (A × C)
(vi) matches with (e)
