A proof that if $S \cap T = S$, then $S \subseteq T$ I have to prove the following:

If $S \cap T = S$, then $S \subseteq T$.

I have no idea where to start. Here's what I have done so far:
Suppose $S$ and $T$ are two sets and assume the fact that $S \cap T = S$.
Let $(x \in S \cap T)$, then:
$(x \in S) \wedge (x \in T) ≡ (x \in S)$
I am stuck here. What should I do to get $S \subseteq T$?

Remember that $S \subseteq T$ means that $x \in S$ implies $x \in T$. So in your proof you start by supposing $x \in S$, and then use the assumption that $S \cap T = S$ to show that $x \in T$. Why might this be the case? To get you started, notice that we have $x \in S \cap T$ since $S \cap T = S$. Now you can use the definition of $S \cap T$ to see that we must have $x \in T$.
