Q6 of 86 Page 26

Assume that P (A) = P (B). Show that A = B

We have to show that: A = B

Let us now assume, P (A) = P (B)


Let,



∴


Now, we have:


C ⊂ B


∴


∴ A ⊂ B


Similarly, we have:


B ⊂ A


∴ A = B


More from this chapter

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4

Show that the following four conditions are equivalent:

(i) A ⊂ B (ii) A – B = ϕ (iii) A ∪ B = B


(iv) A ∩ B = A

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Show that if A ⊂ B, then C – B ⊂ C – A.

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

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Show that for any sets A and B,

A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)