1. **Stating the problem:** We have three newspapers M (Mirror), C (Citizen), and T (Times). Given: - Number of people who read M = 55 - Number of people who read C = 45 - Number of people who read T = 39 - Number of people who read M and T = 19 - Number of people who read C and M = 15 - Number of people who read C and T = 14 - Number of people who read all three M, C, and T = 4 - Number of people who read none = 5 We need to find: (a) Number who read Mirror only (b) Number who read Citizen but not Mirror (c) Total number of people interviewed 2. **Define variables for intersections:** Let: - $|M| = 55$ - $|C| = 45$ - $|T| = 39$ - $|M \cap T| = 19$ - $|C \cap M| = 15$ - $|C \cap T| = 14$ - $|M \cap C \cap T| = 4$ - $N_{none} = 5$ 3. **Calculate only Mirror readers** Using the Principle of Inclusion-Exclusion: Number who read **only** Mirror: $$|M| - |M \cap C| - |M \cap T| + |M \cap C \cap T| = 55 - 15 - 19 + 4 = 25$$ 4. **Calculate Citizen readers but not Mirror** This includes people who read only Citizen and those who read Citizen and Times but not Mirror. Number who read Citizen but not Mirror: $$|C| - |C \cap M| = 45 - 15 = 30$$ 5. **Calculate total number of people interviewed** Using Inclusion-Exclusion formula for three sets: $$|M \cup C \cup T| = |M| + |C| + |T| - |M \cap C| - |C \cap T| - |M \cap T| + |M \cap C \cap T|$$ $$= 55 + 45 + 39 - 15 - 14 - 19 + 4 = 95$$ Adding people who read none: $$Total = |M \cup C \cup T| + N_{none} = 95 + 5 = 100$$ **Final answers:** - (a) Mirror only = 25 - (b) Citizen but not Mirror = 30 - (c) Total interviewed = 100