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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) – Cwhich 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» (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. |
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