Q. 35.0( 5 Votes )

If A and B are no

Answer :

Given: A = B, where A and B are nonempty sets.


Need to prove: A × B = B × A


Let us consider, (x, y) (A × B)


That means, x A and y B


As given in the problem A = B, we can write,


x B and y A


(x, y) (B × A)


That means, (A × B) (B × A) ---- (1)


Similarly we can prove,


(B × A) (A × B) ---- (2)


So, by the definition of set we can say from (1) and (2),


A × B = B × A [Proved]


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