1. **Problem:** In a class of 80 students, every student studies Economics and Geography on both. If 65 students study Economics and 50 study Geography, how many study both subjects? 2. **Formula:** Use the principle of inclusion-exclusion for two sets: $$n(E \cup G) = n(E) + n(G) - n(E \cap G)$$ where $n(E)$ is the number of students studying Economics, $n(G)$ is the number studying Geography, and $n(E \cap G)$ is the number studying both. 3. **Given:** - Total students $n(E \cup G) = 80$ - $n(E) = 65$ - $n(G) = 50$ 4. **Find:** $n(E \cap G)$ 5. **Calculation:** $$80 = 65 + 50 - n(E \cap G)$$ $$n(E \cap G) = 65 + 50 - 80 = 115 - 80 = 35$$ 6. **Answer:** 35 students study both subjects. **Final answer:** (c) 35