Prove that $A - (B \cap C) = (A - B) \cup (A - C)$
How do I go about solving this proof? I've tried a few things but I'm stuck. I don't need the exact proof step by step, just a few hints on how to solve it would really help me.
edit: I tried to solve considering $3$ cases.
If $x$ is an element of $A−(B\cap C)$, then $x$ belongs to $A$ and $x$ doesn't belong to $B\cap C$.
Then, there I considered $3$ possibilites:
$x\in A$ and ($x\in B$ or $x\in C$)
$x\in A$ and ($x\notin B$ or $x\in C$)
$x\in A$ and ($x\in B$ or $x\notin C$)
After that I found that all of these cases satisfied the definition of set difference which states that $A-B$ is equal to the elements of $A$ that are not in $B$. In that case my $B$ is "($B\cap C$)". After that I tried to prove the other side "$(A−B)\cup (A−C)$" but I got lost and didn't know what to do.