1. **Problem Statement:** In a survey of 120 people, the numbers of people reading Computer (C), Electronics (E), and Mechanics (M) are given along with their intersections. We need to find: a) A Venn diagram representation (conceptual explanation). b) The number of people who read at least one of the three subjects. c) The number of people who read exactly one subject. 2. **Given Data:** - Total people surveyed: 120 - $|C|=65$, $|E|=45$, $|M|=42$ - $|C \cap E|=20$, $|C \cap M|=25$, $|E \cap M|=15$ - $|C \cap E \cap M|=8$ 3. **Step a) Venn Diagram Representation:** - The Venn diagram has three overlapping circles labeled C, E, and M. - The center intersection (all three) has 8 people. - The pairwise intersections excluding the triple intersection are: - $|C \cap E| - |C \cap E \cap M| = 20 - 8 = 12$ - $|C \cap M| - |C \cap E \cap M| = 25 - 8 = 17$ - $|E \cap M| - |C \cap E \cap M| = 15 - 8 = 7$ - The number of people in only one subject is found by subtracting intersections from the total in each set: - Only C: $|C| - (|C \cap E| + |C \cap M| - |C \cap E \cap M|) = 65 - (20 + 25 - 8) = 65 - 37 = 28$ - Only E: $|E| - (|C \cap E| + |E \cap M| - |C \cap E \cap M|) = 45 - (20 + 15 - 8) = 45 - 27 = 18$ - Only M: $|M| - (|C \cap M| + |E \cap M| - |C \cap E \cap M|) = 42 - (25 + 15 - 8) = 42 - 32 = 10$ 4. **Step b) Number of people who read at least one subject:** Use the inclusion-exclusion principle: $$ |C \cup E \cup M| = |C| + |E| + |M| - |C \cap E| - |C \cap M| - |E \cap M| + |C \cap E \cap M| $$ Substitute values: $$ = 65 + 45 + 42 - 20 - 25 - 15 + 8 = 152 - 60 + 8 = 100 $$ So, 100 people read at least one subject. 5. **Step c) Number of people who read exactly one subject:** Sum of people who read only one subject: $$ 28 + 18 + 10 = 56 $$ **Final answers:** - Number who read at least one subject: 100 - Number who read exactly one subject: 56 This completes the solution for Exercise 1.