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

Essay

Consider the statement $\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }$
The proof below is the beginning of a proof using the element method for proving that the
set equals the empty set. Complete the proof without using any of the set properties from
Theorem 6.2.2. Proof: Suppose the given statement is false. Then there exist sets $A$ and $B$ such that $( A -$ $B ) \cap B \neq \emptyset$ . Thus there is an element $x$ in $( A - B ) \cap B$ . By definition of intersection,...