Question

(a) shade ( a cup b ).
(b) shade ( (a cap b) ).

Explanation:

Step1: Define complements and union

$A'$ = region not in $A$, $B'$ = region not in $B$. $A' \cup B'$ is all regions in $A'$, $B'$, or both. By De Morgan's Law, this equals $(A \cap B)'$, which is the universal set minus the overlap of $A$ and $B$.

Step2: Shade for (a) $A' \cup B'$

Shade the area outside circle $A$, outside circle $B$, and the area that is outside both (the universal set area not in $A$ or $B$). This excludes only the overlapping part of $A$ and $B$.

Step3: Shade for (b) $(A \cap B)'$

By De Morgan's Law, this is identical to $A' \cup B'$. Shade all regions except the overlapping intersection of $A$ and $B$.

Answer:

(a) Shade the entire universal set $U$ except the overlapping intersection area of circles $A$ and $B$ (this includes the area only in $A$, only in $B$, and the area of $U$ outside both circles).
(b) Shade the entire universal set $U$ except the overlapping intersection area of circles $A$ and $B$ (this is identical to the shading for part (a)).