Question

Consider the following statements for non-empty sets A, B and C. 

1. A – (B – C) = (A – B) ∪ C 

2. A – (B ∪ C) = (A – B) – C

which of the statements given above is /are correct? 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

Answer 1

(b) 2 only

1. A – ( B – C) = A – (B ∩ C′) 

= A ∩ (B ∩ C′)′ 

= A ∩ (B′ ∪ (C′)′) 

= A ∩ (B′ ∪ C) 

(Α – Β) ∪ C = (A ∩ B′) ∪ C 

Thus, A – ( B – C) ≠ (A – B) ∪ C 

2. A – ( B ∪ C) = A ∩ (B ∩ C)′ 

= A ∩ (B′ ∩ C′) 

(A – B) – C = (A ∩ B′) – C 

= A ∩ B′ ∩ C′ 

⇒ A – (B ∪ C) = (A – B) – C 

Associative property.