Q. 73.7( 3 Votes )

Prove that A × B

Answer :

Let A and B be any two sets such that


A × B = {(a, b): a ϵ A, b ϵ B}


Now,


B × A = {(b, a): a ϵ A, b ϵ B}


A × B = B × A


(a, b) = (b, a)


We can see that this is possible only when the ordered pairs are equal.


Therefore,


a = b and b = a


Hence, Proved.


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