Answer :

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

Now let us consider (a_{1}, b_{1}), (a_{2}, b_{2}) ϵ A × B

Such that f(a_{1}, b_{1}) = f(a_{2}, b_{2})

⇒ (b_{1}, a_{1}) = (b_{2}, a_{2})

⇒ b_{1} = b_{2} and a_{1} = a_{2}

⇒ (a_{1}, b_{1}) = (a_{2}, b_{2})

⇒ 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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