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


11
1