Let $A, B$ and $C$ be sets. If $a$ is the proposition $x\in A$, $b$ is the proposition $x\in B$, and $c$ is the proposition $x\in C$, write down a proposition involving $a, b$ and $c$ that is logically equivalent to $$x \in A \cup (B − C).$$
Attempt: $a\cup (b \cap \neg c)$. Can someone please clarify?
On
$\cup$ and $\cap$ are operations on sets, but you want operations on propositions, so you want to use $\lor$ and $\land$. In fact, you already figured out to use $\neg$ as an operation on a claim, rather than to stick to $B-C$ or, equivalently, $B \cap C'$.
So, you should use $a \lor (b \land \neg c)$
Use $\land$ and $\lor$ for the logical connectors, $\lnot$ for not etc.
Then your idea is essentially correct but I'd write
$$a \lor (b \land \lnot c)$$
Logically this is the same as
$$a \lor \lnot(b \to c)$$
so that's one alternative that looks less trivial.