Question

Let A and B be sets . Show that f : A X B ---> B X A such that f (a,b) = (b,a) is bijective function.

Answer 1

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solution:--

f: A × B → B × A is defined as f(a, b) = (b, a).


∴ f is one-one.

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

Then, there exists (a, b) ∈A × B such that f(a, b) = (b, a). [By definition of f]

∴ f is onto.

Hence,f is bijective.