I find these problems easy enough to understand, I just have trouble with proofs that make sense.

For example, if I wanted to prove:

$\displaystyle (C \cup D) \setminus (C\cap D)=(C\setminus D)\cup(D\setminus C)$

Can I write:

$\displaystyle (C \cup D)-(C\cap D)=\{x:x\in C$ or $\displaystyle x\in D\}\wedge \{x\in C:x\not\in D\}\wedge \{x\in D:x\not\in C\}$

$\displaystyle \Rightarrow ( \forall x \in C)(x \in (C\cup D^c ))$ and $\displaystyle ( \forall x \in D)(x \in (D\cup C^c ))$

Hence,

$\displaystyle (C \cup D)\setminus (C\cap D)= (C\cup D^c ) \cup (D\cup C^c ) = (C\setminus D)\cup(D\setminus C)$