Proof work - Topology Images and Inverse Images

uncledub

1. Let f:X->Y be a function and let U be a subset of X and V a subset of X. Prove that f(U) - f(v) is a subset of f(U-v).

3. The attempt at a solution

Suppose x belongs to f(U-v), then f(x) belongs to U-V and then f(x) does not belong to V so f(x) belongs to U. Then it holds that f(U) - f(v) is a subset of f(U-V).

I will be honest I am totally lost. This is my first Masters class and I am doing it online. I cant wait for the semester to end so I can switch Masters programs. But I need to make it through first.

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