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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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