1. **State the problem:** We have 120 students studying Mathematics (M), Economics (E), and Computer Studies (C) with given overlaps. We want to represent this information using a three-set Venn diagram. 2. **Given data:** - $|M|=50$ - $|E|=60$ - $|C|=40$ - $|M \cap E|=20$ - $|M \cap C|=15$ - $|E \cap C|=10$ - $|M \cap E \cap C|=5$ 3. **Important rule:** To find the number of students in exactly two subjects, subtract those in all three from the pairwise intersections. 4. **Calculate students in exactly two subjects:** - $|M \cap E| - |M \cap E \cap C| = 20 - 5 = 15$ - $|M \cap C| - |M \cap E \cap C| = 15 - 5 = 10$ - $|E \cap C| - |M \cap E \cap C| = 10 - 5 = 5$ 5. **Calculate students in only one subject:** - Only $M = |M| - (\text{exactly } M \cap E + \text{exactly } M \cap C + |M \cap E \cap C|) = 50 - (15 + 10 + 5) = 20$ - Only $E = 60 - (15 + 5 + 5) = 35$ - Only $C = 40 - (10 + 5 + 5) = 20$ 6. **Calculate students studying none of the three subjects:** Total students = 120 Sum of all groups = Only $M +$ Only $E +$ Only $C +$ Exactly two-subject groups + All three = $20 + 35 + 20 + 15 + 10 + 5 + 5 = 110$ None = $120 - 110 = 10$ 7. **Summary for Venn diagram:** - Only $M$: 20 - Only $E$: 35 - Only $C$: 20 - Exactly $M \cap E$: 15 - Exactly $M \cap C$: 10 - Exactly $E \cap C$: 5 - All three: 5 - None: 10 This completes the representation of the data for the three-set Venn diagram.