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

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

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We have f : (A × B) → (B × A) such that f(a, b) = (b, a).

(a) ∴ f{a1, b1) = (b1, a1), f(a2, b2) = (b2, a2) and

f(a1, b1) = f(a2, b2) ⇒ (b1,1) = (b2, a2)

⇒ b1 = b2 and a1 = a2

∴ f is onto

Thus, f is one-one and onto, ie. it is bijective.

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