Chapter 6.1, Problem 1ES

To determine

(a)

Proof: Suppose $A\text{ and }B$ are any sets. To show that $A-B\subseteq A$, we must show that every element in __(1)__ is in __(2)__. But any element in $A-B$ is in ___(3)___ and not in ___(4)___(by definition of $A-B$ ). In particular, such an element is in $A$.

To determine

(b)

Suppose $A\text{ and }B$ are any sets and $x\in A-B$. [we must show that $\left(1\right)$ ]. By definition of set difference, $x\in \left(2\right)\text{ and }x\notin \left(3\right)$. In particular, $x\in \left(4\right)$ [which is what was to be shown].