1. **Problem statement:** There are 25 students who took math and science exams. 17 passed science, 8 passed both math and science, and 3 did not pass either exam. We need to find how many passed math. 2. **Define variables:** Let $M$ be the number of students who passed math, $S=17$ the number who passed science, $B=8$ the number who passed both, and $N=3$ the number who passed neither. 3. **Total students:** Total students $T=25$. 4. **Use the formula for union of two sets:** $$|M \cup S| = |M| + |S| - |M \cap S|$$ 5. **Students who passed at least one subject:** $$|M \cup S| = T - N = 25 - 3 = 22$$ 6. **Substitute known values:** $$22 = M + 17 - 8$$ 7. **Solve for $M$:** $$M = 22 - 17 + 8 = 13$$ **Answer:** 13 students passed math.