1.

For any two sets A and B, prove that A – (A – B) = A ∩ B

Answer»

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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