And my answer was why was my answer wrong the grader said it

And my answer was:

why was my answer wrong? the grader said it was due to \"You assumed that f,g and fog are all invertible which is not true.\" but to the given I was able to deduce this answer.

27. Let f: X Y and g: Y Z. Is the following prop erty true or false? For all subsets C in Z, (g of) (C) f-1(g (C). Justify your answer.

Solution

fog may not be even defined without any restrictions because f has domain X but g has Co-domain Z. So g(y) would give image in Z and f has to take elements from Z then.