Originally Posted by

**mastermind2007** Hi enriquestefanini,

well, by the definition of a function $\displaystyle f: G \rightarrow H $, and you have g $\displaystyle \in$ G,

then there is at most **one** image f(g) = h $\displaystyle \in$ H (there cannot be two distinct elements of H being

the image of g, since this would be in contrary to the definition of a function).

So if you have at least two elements in the image of f, e.g. $\displaystyle im(f) = \{h_1 , h_2\} $, then

you have at least two different elements of G. Then it follows that M cannot be 1 alone, since if it was,

there would be only **one** element in f(M).

Further, the image f(N) $\displaystyle \subset $ H.

Is that clear to you now?