Question

shade ( a cup b ) on the venn diagram.

Explanation:

Step1: Define complement of A

$A'$ = All elements not in $A$ (region outside red circle, including part of $B$ and universal set $U$ outside both circles)

Step2: Define complement of B

$B'$ = All elements not in $B$ (region outside blue circle, including part of $A$ and universal set $U$ outside both circles)

Step3: Find union $A' \cup B'$

$A' \cup B'$ = All elements in $A'$ OR $B'$: this includes the part of $A$ not overlapping with $B$, the part of $B$ not overlapping with $A$, and the entire universal set region outside both circles. The only unshaded region is the overlap of $A$ and $B$.

Answer:

Shade three regions:

1. The portion of circle $A$ that does not overlap with circle $B$
2. The portion of circle $B$ that does not overlap with circle $A$
3. The area inside the universal set $U$ that is outside both circles $A$ and $B$

(The overlapping intersection area of $A$ and $B$ remains unshaded.)