Given nine courses CS1, CS2, CS3, P1,P2, P3, M1, M2 and M3, and the following listing which shows courses for which exams cannot be at the same time due to students' course selections: Students who pursue Course CS1 also pursue CS3 and P1. Those who pursue Course CS2 also pursue CS1, P2, M2 and M3. Students who pursue Course P3 also pursue CS2, CS3 and P1. Those who pursue Course M1 also pursue M2, P1 and CS3. Students who pursue Course M2 also pursue M1, M3, P2 and CS2. Those who pursue Course M3 also pursue M2, CS2 and P1. By constructing a graph to represent the above information determine which M courses (M1, M2 or M3) may be held at the same time? Select one: a. M1 and M3 b. M2 and M3 M course may have exam same time as another without a clash. d. M1 and M2 e. M1, M2 and M3

To determine which M courses (M1, M2, M3) may be held at the same time without a clash, we can represent the relationships between the courses as a graph. In this graph, each course is a node, and an edge between two nodes indicates that those courses cannot be held at the same time. From the information provided, we can summarize the relationships as follows: 1. **CS1** → CS3, P1 2. **CS2** → CS1, P2, M2, M3 3. **P3** → CS2, CS3, P1 4. **M1** → M2, P1, CS3 5. **M2** → M1, M3, P2, CS2 6. **M3** → M2, CS2, P1 Now, let's analyze the relationships specifically for the M courses: - **M1** cannot be held at the same time as: - M2 (because M1 → M2) - P1 (because M1 → P1) - CS3 (because M1 → CS3) - **M2** cannot be held at the same time as: - M1 (because M2 → M1) - M3 (because M2 → M3) - P2 (because M2 → P2) - CS2 (because M2 → CS2) - **M3** cannot be held at the same time as: - M2 (because M3 → M2) - CS2 (because M3 → CS2) - P1 (because M3 → P1) Now, let's summarize the clashes: - M1 clashes with M2. - M2 clashes with M1 and M3. - M3 clashes with M2. From this analysis, we can conclude that: - **M1 and M2 cannot be held at the same time.** - **M2 and M3 cannot be held at the same time.** - **M1 and M3 can be held at the same time.** Thus, the only M courses that may be held at the same time without a clash are **M1 and M3**. Therefore, the correct answer is: **a. M1 and M3**.