Six delegates—Alan, Bina, Farah, George, Harish, and Indu—are to be divided into two committees, Committee X and Committee Y, with exactly three members in each committee. The assignment must satisfy the following conditions:
1. Alan and Bina cannot be assigned to the same committee.
2. If Farah is assigned to Committee X, then George must be assigned to Committee Y.
3. Harish and Indu must be assigned to the same committee.
4. Alan is assigned to Committee X.
Which of the following delegates MUST be assigned to Committee X?
- HarishAnswer
- BBina
- CFarah
- DGeorge
Answer
Harish must be assigned to Committee X.
Because Alan is in Committee X, Bina must be in Committee Y. If Harish and Indu were placed in Committee Y, Committee Y would be full with Bina, Harish, and Indu. That would force Farah and George into Committee X. However, placing Farah in Committee X requires George to be in Committee Y, which creates a contradiction. Therefore, Harish and Indu must be in Committee X.
Step-by-Step Solution
Key Concept
Analytical Grouping and Constraint Satisfaction
Estimated Time:1m 30s