Prove that $A \cap B$ is a subset of $A$.
Would I go around this by saying that $S \subseteq A$ and then by hypothesis belongs to $B$ as well?
Or would I do it with values of $X$?
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Mar 26 '20 at 00:01
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$A$ is a subset of $C$, per definition, means that every element of $A$ is an element of $C$. Since for every element $x$ of $A \cap B$, $x$ is an element of $A$, this shows the required. – hteica Mar 26 '20 at 00:12