## Thinking Mathematically (6th Edition)

$\left\{a, e\right\}$
RECALL: (1) $\cup$ represents union of sets. The union of two sets is a set that contains the combined elements of the two sets. (2) $\cap$ represents intersection of sets. The intersection of two sets is a set that contains all the elements that are common to the two sets. To find the elements of the given set, you have to (i) find the union of $A$ and $B$, then (ii) find the intersection of $A\cup B$ and $C$ afterwards. Note that: $A \cup B =\left\{a, b, c, d, e, f\right\}$ Thus, $(A \cup B) \cap C \\= \left\{a, b, c, d, e, f\right\} \cap \left\{a, e, g\right\} \\= \left\{a, e\right\}$