1. **State the problem:** We have two sets: \(A\) = multiples of 3, \(B\) = even numbers, and the universal set is \(\{2,3,4,6,8,9,10,12,14,15\}\). 2. **Find \(n(A)\):** Count elements in \(A\) (multiples of 3) from the universal set. \(A = \{3,6,9,12,15\}\) \(n(A) = 5\) 3. **Find \(n(B)\):** Count elements in \(B\) (even numbers) from the universal set. \(B = \{2,4,6,8,10,12,14\}\) \(n(B) = 7\) 4. **Find \(n(A \cap B)\):** Elements common to both \(A\) and \(B\) (multiples of 3 and even numbers). \(A \cap B = \{6,12\}\) \(n(A \cap B) = 2\) 5. **Find \(n(A \cup B)\):** Use the formula $$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$ Substitute values: $$n(A \cup B) = 5 + 7 - 2 = 10$$ **Final answers:** - \(n(A) = 5\) - \(n(B) = 7\) - \(n(A \cup B) = 10\)