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1. |
Use the properties of sets to prove that for all the sets A and BA – (A ∩ B) = A – B |
Answer» We have A – (A ∩ B) = A ∩ (A ∩ B)′ (since A – B = A ∩ B′) = A ∩ (A′ ∪ B′) [by De Morgan’s law) = (A ∩ A′) ∪ (A ∩ B′) [by distributive law] = φ ∪ (A ∩ B′) = A ∩ B′ = A – B |
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