Question 1
A PhD thesis defense requires all 5 committee members to be present. Their availability (slots 1-8):
- Prof. C: Slots 4, 7
- Prof. A: Slots 4, 3, 8, 2
- Prof. D: Slots 4, 6, 1
- Prof. E: Slots 6, 3, 4, 7
- Prof. B: Slots 1, 4, 6, 5
What is the earliest slot when all can attend?
Step-by-step solution:
1. Find intersection of availability:
Prof. C: [4, 7]
∩ Prof. A: [2, 3, 4, 8]
∩ Prof. D: [1, 4, 6]
∩ Prof. E: [3, 4, 6, 7]
∩ Prof. B: [1, 4, 5, 6]
= [4]
2. Earliest common slot: Slot 4
Answer: Slot 4
1. Find intersection of availability:
Prof. C: [4, 7]
∩ Prof. A: [2, 3, 4, 8]
∩ Prof. D: [1, 4, 6]
∩ Prof. E: [3, 4, 6, 7]
∩ Prof. B: [1, 4, 5, 6]
= [4]
2. Earliest common slot: Slot 4
Answer: Slot 4