Help with Subset Problem So I'm "supposed to show that":
$(A \cup B)  \subseteq (A \cup B \cup C)$.
For $(A \cup B)$, $x \in A \cup B$ and therefore $x \in A \lor x \in B$. For
$(A \cup B \cup C )$ , $x \in A \cup B \cup C$ and therefore $x \in A \lor x \in B \lor x \in C$. I'm not quite sure how to explain my results.  The best I can come up with is because $x$ is an element of set $A$ or set $B$ or set $C$,  $(A \cup B)$ is a subset of $(A \cup B \cup C)$. How can I explain this better?
Follow up question:
Thanks for the explanations and I'd like to get help on another one.
$(A \cap B \cap C) \subseteq (A \cap B)$.
So for $(A \cap B)$, $x \in A \land x \in B$. And $x \in A$ and $ x \in B$ must be true. Can I assume that  $(A \cap B \cap C)$ must be true as well if it is a subset of $(A \cap B)$ and that $x \in C$ must be true?

HINT: Note that $Y\subset X$ if and only if $Y\cap X=Y $
