Hmm, there's something fishy about this. With the conditional statement "if [tex]X\subseteq im(A)[/tex] then A is surjective". Which do they mean:
1) Take an A fixed and X fixed. If [tex]X\subseteq im(A)[/tex] for this specific X and A, then A is surjective.
or
2) Take X fixed. If [tex]X\subseteq im(A)[/tex] for any A, then this A is surjective.
I think they mean (2). Since (1) wouldn't make any sense. But they way you frazed the question, kind of suggest (1)...
