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?)