Question

shade $(a cup b) cup (a cap c)$ on the venn diagram.

Explanation:

Step1: Simplify the set expression

Using set properties: $(A \cup B) \cup (A \cap C) = A \cup B$
(Reason: $A \cap C$ is a subset of $A$, so adding it to $A \cup B$ does not change the set)

Step2: Identify regions to shade

Shade all of circle $A$ (including its overlaps with $B$ and $C$) and all of circle $B$ (including its overlap with $A$).

Answer:

Shade the entire circle $A$, the entire circle $B$, and the overlapping regions between $A$ and $B$, $A$ and $C$. (This is equivalent to shading all elements in $A$ or $B$.)