1.

Show that for any sets A and B, A ∪ (B – A) = A ∪ B

Answer»

Let x ϵ A ∪ (B – A) 

⇒ x ϵ A or x ϵ (B–A) 

⇒ X ϵ A or x ϵ B or x ∉ A 

⇒ x ϵ A or x ϵ B 

⇒ x ϵ (A ∪ B) 

∴ A ∪ (B – A) ⊂ (A ∪ B)…….(1) 

Let and x ϵ (A ∪ B) 

⇒ x ϵ A or x ϵ B 

⇒ x ϵ A or x ϵ B and x ∉ A 

⇒ x ϵ A or x ϵ B–A 

⇒ x ϵ A ∪ (B–A) 

∴ (A ∪ B) ⊂A ∪ (B – A)…….(2) 

From (1) and(2), we get 

A ∪ (B – A) = A ∪ B.



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