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 Mentor P: 18,027 Hmm, there's something fishy about this. With the conditional statement "if $$X\subseteq im(A)$$ then A is surjective". Which do they mean: 1) Take an A fixed and X fixed. If $$X\subseteq im(A)$$ for this specific X and A, then A is surjective. or 2) Take X fixed. If $$X\subseteq im(A)$$ 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)...