Q23 of 24 Page 1

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)

It is given in the question that,


A and B are sets such that


And, for some set X


Now, we have to show that A = B


As it can be seen that,


= (By using distributive law)


=


= (i)


Now, we have:



=


= (By using distributive law)


=


=


(ii)


∴ From the equation (i) and (ii), we have


A = B

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