Question 1
A PhD thesis defense requires all 4 committee members to be present. Their availability (slots 1-8):
- Prof. D: Slots 4, 7, 3, 1
- Prof. A: Slots 2, 1
- Prof. C: Slots 1, 6, 2, 4
- Prof. B: Slots 4, 1
What is the earliest slot when all can attend?
Step-by-step solution:
1. Find intersection of availability:
Prof. D: [1, 3, 4, 7]
∩ Prof. A: [1, 2]
∩ Prof. C: [1, 2, 4, 6]
∩ Prof. B: [1, 4]
= [1]
2. Earliest common slot: Slot 1
Answer: Slot 1
1. Find intersection of availability:
Prof. D: [1, 3, 4, 7]
∩ Prof. A: [1, 2]
∩ Prof. C: [1, 2, 4, 6]
∩ Prof. B: [1, 4]
= [1]
2. Earliest common slot: Slot 1
Answer: Slot 1