Q9 of 86 Page 26

Using properties of sets, show that:

(i) A ∪ (A ∩ B) = A


(ii) A ∩ (A ∪ B) = A.

(i) We have to show that:



Now, we know that:




∴ (i)


Also, we have:


(ii)


Hence, by using equation (i) and (ii) we have:



(ii) We have to show that:




=



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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)

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Show that A ∩ B = A ∩ C need not imply B = C.

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Let A and B be sets. If A ∩ X = B ∩ X = f and A ∪ X = B ∪ X for some set X, show that A = B.

(Hints A = A ∩ (A ∪ X) , B = B ∩ (B ∪ X) and use Distributive law)