Thinking Mathematically (6th Edition)

The given sets aren't equal for all sets $A$ and $B$.
Regions in $A'$ (all the regions not in $A$) are: $III, IV$ Regions in $B$ are: $II, III$ Regions in $A'\cup B$ are: $II, III, IV$ Regions in $A$ are: $I, II$ Regions in $B'$ (all the regions not in $B$) are: $I, IV$ Regions in $A\cap B'$ are: $I$ The elements of $A'\cup B$ and $A\cap B'$ are in different regions; therefore, those two sets aren't equal for all sets $A$ and $B$.