Consider the Statement $$\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }$$

Essay

Consider the statement $$\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }$$
Complete the proof begun below in which the given statement is derived algebraically from
the properties listed in Theorem 6.2.2. Be sure to give a reason for every step that exactly justifies what was done in the step: Proof:
Let $A$ and $B$ be any sets. Then the left-hand side of the equation to be shown is

which is the right-hand side of the equation to be shown. [Hence the given statement is true.]
(The number of lines in the outline shown above works for one version of a proof. If you write
a proof using more or fewer lines, be sure to follow the given format, supplying a reason for
every step that exactly justifies what was done in the step.)