Q12 of 162 Page 1

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

A’ ∪ B = U A ⊂ B

To show: A⊂B


⇒ x ∉ A


⇒ x ϵ A and A ⊂ U


⇒ x ϵ A


⇒ x ϵ (A’ ∪ B) [∵ U = A’∪ B]


⇒ x ϵ A’ or x ϵ B


But, x ∉ A’,


∴ x ϵ B


Thus, x ϵ A ⇒ x ϵ B


This is true for all x ϵ A


∴ A ⊂ B


More from this chapter

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10

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

 11

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

 12

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

B’ ⊂ A’ A ⊂ B

 13

Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer.