Q11 of 162 Page 1

Using properties of sets, show that for any two sets A and B, (A ∪ B) ∩ (A ∪ B’) = A.

We need to show (A ∪ B) ∩ (A ∪ B’) = A.


Now,


(A ∪ B) ∩ (A ∪ B’) = ((A ∪ B) ∩ A) ∩ B’.


= (A ∩ A) ∪ (B ∩ A)) ∩B’


= A ∩ B’


= A.


More from this chapter

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9

For any two sets A and B, prove that: A ∩ B = ϕ A B’.

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If A and B are sets, then prove that A – B, A ∩ B and B – A are pair wise disjoint.

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For any two sets of A and B, prove that:

A’ ∪ B = U A ⊂ B

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For any two sets of A and B, prove that:

B’ ⊂ A’ A ⊂ B