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

Given, f : A × B → B × A  Such that  f : (a, b) = f(b, a)

(a)   f (a₁, b₁) = (b₁, a₁),f (a₂, b₂) = (b₂, a₂)

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

⇒b₁ = b₂,    a₁, a₂ ⇒ f is one-one.

(b) Every element (p, q) belonging to its codomain has pre-image in its domain as (q, p). f is onto.