# Let $A, B$ and $X$ be sets. Prove that if $A ∪ B ⊆ X$ then $A ⊆ X$.

I have just started learning set theory and I've been trying to learn how to do proofs, however I really can't figure out

I've been trying to answer a simple one:

Let $A, B$ and $X$ be sets. Prove that if $A ∪ B ⊆ X$ then $A ⊆ X$.

If anyone can point me in the right direction (e.g. a strategy to use when going about these types of proofs) or provide a worked example of a different proof.

First, assume that $A \cup B$ is a subset of $X$. Then assume $x$ is an arbitrary element of $A$, and try to prove that $x \in X$, using your first assumption. Since $x$ was arbitrary, it then follows that $A$ is a subset of $X$.