1. **State the problem:** We have 35 students in total. - 18 students play hockey. - 12 students play both hockey and tennis. - 15 students play neither hockey nor tennis. We need to find the number of students who play tennis. 2. **Use the formula for sets:** Let $H$ be the set of students who play hockey, $T$ be the set of students who play tennis. Total students = $|H \cup T| +$ students who play neither. We know: $$|H| = 18, \quad |H \cap T| = 12, \quad \text{neither} = 15, \quad \text{total} = 35.$$ 3. **Find $|H \cup T|$:** $$|H \cup T| = \text{total} - \text{neither} = 35 - 15 = 20.$$ 4. **Use the union formula:** $$|H \cup T| = |H| + |T| - |H \cap T|.$$ Substitute known values: $$20 = 18 + |T| - 12.$$ 5. **Solve for $|T|$:** $$20 = 6 + |T| \implies |T| = 20 - 6 = 14.$$ **Answer:** 14 students play tennis.