Answer :

It is given that f : A × B B × A is defined as f (a, b) = (b, a)

Now let us consider (a1, b1), (a2, b2) ϵ A × B


Such that f(a1, b1) = f(a2, b2)


(b1, a1) = (b2, a2)


b1 = b2 and a1 = a2


(a1, b1) = (a2, b2)


f is one-one.


Now, let (b, a) ϵ B × A be any element.


Then, there exists (a, b) ϵ A × B such that f(a, b) = (b, a)


f is onto.


Therefore, f is bijective.


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