Q4 of 162 Page 1

For any two sets A and B, prove that

A – (A – B) = A ∩ B

Let x ϵ A–(A–B) ⬄ x ϵ A and x ∉ (A–B)


⬄ x ϵ A and x ∉ (A ∩ B)


⬄ x ϵ A∩(A ∩ B)


⬄ x ϵ (A ∩ B)


∴ A–(A–B) = (A ∩ B)


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For any two sets A and B, prove that

(A ∪ B) – B = A – B

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A – (A ∩ B) = A – B

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For any two sets A and B, prove that

A ∪ (B – A) = A ∪ B

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(A – B) ∪ (A ∩ B) = A