Subsets and equality
Hello I'm new to set theory and I want to know how I can solve the following question
Let $U$ be a universe and $A,B$ and $C$ be subsets of $U$. Prove or disprove:
$$(A \cup B) = (A \cup C)\implies B = C$$
I'm looking at the "Typical element" Method of proving this statement but I'm confused on how to go about it or if it is even the correct method to be using.