For any two non-empty sets A and B drawn from the same universe, U, let Z be the set defined as

$\displaystyle Z = (A \frown \sim B) \smile (\sim A \frown B)$

Z is the symmetric difference of A and B.

Through the use of Venn diagrams show the following:
- Z could equal $\displaystyle \emptyset$. (two shaded, separate circles?)
- Z could never equal B. (Shade in A and U?)
- Z can equal U. (Shade in $\displaystyle Z = (A \frown \sim B) \smile (\sim A \frown B)$ and U?)