Q4 of 162 Page 1

For any two sets A and B, prove that

(A – B) ∪ (A ∩ B) = A

Let x ϵ A


Then either x ϵ (A–B) or x ϵ (A ∩ B)


⇒ x ϵ (A–B) ∪ (A ∩ B)


∴ A ⊂ (A – B) ∪ (A ∩ B)….(1)


Consverly,


Let x ϵ (A–B) ∪ (A ∩ B)


⇒ x ϵ (A–B) or x ϵ (A ∩ B)


⇒ x ϵ A and x ∉ B or x ϵ B


⇒ x ϵ A


∴ (A–B) ∪ (A ∩ B) ⊂ A……….(2)


∴ From (1) and (2), We get


(A–B) ∪ (A ∩ B) =A


More from this chapter

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A – (A – B) = A ∩ B

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A ∪ (B – A) = A ∪ B

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If A and B are two sets such that n (A ∪ B) = 50, n(A) = 28 and n(B) = 32, find n (A ∩ B).

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