1.

If f: A → B is an injection such that range of f = {a}. Determine the number of elements in A.

Answer»

One – One Function: – A function f: A → B is said to be a one – one functions or an injection if different elements of A have different images in B.

So, f: A → B is One – One function

⇔ a≠b

⇒ f(a)≠f(b) for all a, b ∈ A

⇒ f(a) = f(b)

⇒ a = b for all a, b ∈ A

Here, Range {f} = {a}

Since it is injective map, different elements have different images.

Thus A has only one element



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