Let E represent Economics, M represent Mathematics, and G represent Geography.

Here's the solution to the problem. Let E represent Economics, M represent Mathematics, and G represent Geography. The total number of students is n(U) = 70. All students offer at least one subject, so n(E M G) = 70. We are given the following information: 1. n(E only) = 6 2. n(E M^c) = 18 (Economics but not Mathematics) 3. n(E G) = 38 (Economics and Geography) 4. n(E) = 53 (Economics) 5. n(G) = 50 (Geography) 6. n(M G) = 34 (Mathematics and Geography) Let's denote the number of students in each region of the Venn diagram as follows: • a = n(E only) • b = n(M only) • c = n(G only) • d = n(E M G^c) (Economics and Mathematics only) • e = n(E G M^c) (Economics and Geography only) • f = n(M G E^c) (Mathematics and Geography only) • g = n(E M G) (Economics, Mathematics, and Geography) Using the given information to find the values for each region: Step 1: From (1), a = 6. Step 2: From (2), n(E M^c) = a + e = 18. Since a=6, we have 6 + e = 18 e = 12. Step 3: From (3), n(E G) = e + g = 38. Since e=12, we have 12 + g = 38 g = 26. Step 4: From (4), n(E) = a + d + e + g = 53. Since a=6, e=12, g=26, we have 6 + d + 12 + 26 = 53 d + 44 = 53 d = 9. Step 5: From (6), n(M G) = f + g = 34. Since g=26, we have f + 26 = 34 f = 8. Step 6: From (5), n(G) = c + e + f + g = 50. Since e=12, f=8, g=26, we have c + 12 + 8 + 26 = 50 c + 46 = 50 c = 4. Step 7: Since all students offer at least one subject, $n(E M G) = a + b + c + d +