1. The problem asks for the intersection of two sets $A$ and $B$, where $A = \{1, 2, 3\}$ and $B = \{3, 4, 5\}$. The intersection of two sets, denoted $A \cap B$, is the set of elements that are common to both $A$ and $B$. 2. The formula for the intersection of two sets is: $$A \cap B = \{x : x \in A \text{ and } x \in B\}$$ 3. To find $A \cap B$, we look for elements that appear in both $A$ and $B$: - $1$ is in $A$ but not in $B$ - $2$ is in $A$ but not in $B$ - $3$ is in both $A$ and $B$ - $4$ is in $B$ but not in $A$ - $5$ is in $B$ but not in $A$ 4. Therefore, the intersection $A \cap B = \{3\}$. 5. Comparing with the options given, the correct answer is c. $\{3\}$.