1. **Problem Statement:** We have a survey of 200 students about reading three newspapers: Imvaho (I), New Times (N), and Daily Times (D). Given data: - $|I|=96$, $|N|=52$, $|D|=72$ - $|N \cap I|=16$, $|N \cap D|=10$, $|I \cap D|=8$ - $|\text{none}|=9$ We need to find: (a) Venn diagram illustration (not drawn here but described) (b) Number of students who read all three newspapers (c) Number who read New Times and Imvaho only (d) Number who read only Daily Times 2. **Formula and Rules:** Use the principle of inclusion-exclusion for three sets: $$|I \cup N \cup D| = |I| + |N| + |D| - |I \cap N| - |N \cap D| - |I \cap D| + |I \cap N \cap D|$$ Total students = $|I \cup N \cup D| + |\text{none}| = 200$ 3. **Step-by-step Solution:** (a) Venn diagram would have three overlapping circles labeled I, N, D with intersections representing the given numbers. (b) Let $x = |I \cap N \cap D|$ be the number of students reading all three. Using inclusion-exclusion: $$|I \cup N \cup D| = 200 - 9 = 191$$ $$191 = 96 + 52 + 72 - 16 - 10 - 8 + x$$ Simplify: $$191 = 220 - 34 + x$$ $$191 = 186 + x$$ $$x = 191 - 186 = 5$$ (c) Number who read New Times and Imvaho only: $$|N \cap I| - |I \cap N \cap D| = 16 - 5 = 11$$ (d) Number who read only Daily Times: $$|D| - |I \cap D| - |N \cap D| + |I \cap N \cap D| = 72 - 8 - 10 + 5 = 59$$ **Final answers:** - (b) $5$ - (c) $11$ - (d) $59$