# Let A and B be sets. Show that f : A × B → B × A such that f (a, b) = (b, a) is bijective function.

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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