Question

If $A,B$ are any two sets and $C\subset A\bigcup B$. Then is it true that $C\subseteq A$ or $C\subseteq B$?

Answer 1

Let

$x\in C$

Then $x\in (A\cup B)$

$x\in A$ or $x\in B$

$C\in A$ or $C\in B$

Therefore, $x$ is general element of $C$.