Does $a$ belong to $X=\{a,1,b\}$? Is $a$ a subset of $X$? I know this is pretty evident, but somehow I feel uncomfortable saying "It's evident" on my test... is there a way to prove (or disprove) this?

If $X=\\{a,1,b\\}$ then $a$ is an _element_ of $X$ so:

$$a\in X$$

$A$ is a subset of $B$ if all elements from $A$ belong to $B$. For example if $A=\\{a,1\\}$, $B=\\{a,1,b\\}$ then $$A\subset B$$

It is possible that $A$ is both a subset and an element of $B$. For example:

$$A=\\{a\\}$$ $$B=\\{a,\\{a\\}\\}$$ $$A\subset B\quad \land \quad A\in B$$