well, by the definition of a function , and you have g G,
then there is at most one image f(g) = h 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. , 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) H.
Is that clear to you now?