Use set equalities to prove $A−(B\cup C) = (A−B)∩(A−C)$ This is what needs to be proved: $$A−(B\cup C) = (A−B)∩(A−C)$$
I've tried working from both sides, but have gotten further from working with the left. Here's my attempt:$$A \cap (B \cup C)^{'}$$ $$A \cap (B^{'} \cap C^{'})$$ $$(A \cap B^{'}) \cap C^{'}$$ $$(A-B)-C$$

You have the following, $A-(B\cup C) = A \cap (B\cup C)^c = A \cap (B^c\cap C^c) = (A \cap B^c) \cap (A\cap C^c) = (A-B)\cap (A-C)$
