1. **Problem Statement:** Given the universal set $e = \{1,2,3,4,5,6,7\}$, set $A$ as even numbers, and set $B$ as prime numbers. 2. **Identify sets:** - $A = \{2,4,6\}$ (even numbers in $e$) - $B = \{2,3,5,7\}$ (prime numbers in $e$) 3. **Find $A \cap B$ (intersection):** Elements common to both $A$ and $B$. $$A \cap B = \{2\}$$ 4. **Find $A \cup B$ (union):** All elements in $A$ or $B$ or both. $$A \cup B = \{2,3,4,5,6,7\}$$ 5. **Explanation:** - The intersection $A \cap B$ contains only the number 2 because it is the only even prime number. - The union $A \cup B$ combines all even and prime numbers from the universal set without repetition. Final answers: - $A \cap B = \{2\}$ - $A \cup B = \{2,3,4,5,6,7\}$