Let \(S\) be a finite set. Then a non-identity function \(f: S \rightarrow S\) can be

Let \(S\) be a finite set. Then a non-identity function \(f: S \rightarrow S\) can be
  1. Injective but not surjective
  2. Surjective but not injective
  3. Bijective but it does not have an inverse function
  4. Data insufficient

Solution

It is given that for a finite set \(\mathrm{S}, f: S \rightarrow S\) is non-identity function, then it can be injective only or surjective only or both or none. So, data is insufficient to answer. Hence, option (d) is correct.

Asked in: AP EAMCET 2020 (21 Sep Shift 2)

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