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Question 8

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

 

Answer

f: A × B → B × A is defined as f(ab) = (ba).

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∴ f is one-one.

Now, let (ba) ∈ B × A be any element.

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

∴ f is onto.

Hence,f is bijective.

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