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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