ACE que booklet

Question

If the set has a finite # of elements, prove that if f maps S onto S1 then which of the following is false??

(a) f is 1-1

(b) f is onto

(c) f is bijection

(d) f is onto and not bijection

Answer 1

Answer : D.. D is False.

For $f : S \rightarrow S$, Where $S$ is Finite... Function $f$ being One-One or Onto or Bijection..All are equivalent. If One is satisfied then other two will automatically satisfy.

Hence, It is Never possible that $f$ can be Onto but Not bijection....NOTE that $S$ must be finite.