Q7 of 86 Page 26

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

Let us assume, A = {0, 1}


And, B = {1, 2}


∴


Now, we have:




∴


Also,


∴


Hence, the given statement is false


More from this chapter

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5

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

 6

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

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Show that for any sets A and B,

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

 9

Using properties of sets, show that:

(i) A ∪ (A ∩ B) = A


(ii) A ∩ (A ∪ B) = A.