I am brain farting on this question pretty hard, I'm asked to determine if
$$A \cup (B - C) = (A \cup B) - (A \cup C)$$
That is, determine if this set equality is true, and if not, which inclusions are true. I was able to show that equality fails by showing '$\subset$' does not hold using a relatively simple example, but I am having issues with opposite inclusion. My attempts began by assuming I had an arbitrary element $x \in (A \cup B) - (A \cup C)$ and tried to work my way down, but I haven't had much success.
Any help or hints would be appreciated, for I am too stubborn to move on to the next part without finishing this one.