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Question
Use the properties of sets to prove that for all the sets A and B
A – (A ∩ B) = A – B
Solution
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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