Question 1
A PhD thesis defense requires all 5 committee members to be present. Their availability (slots 1-8):
- Prof. E: Slots 7, 6
- Prof. C: Slots 5, 3, 6, 8
- Prof. B: Slots 4, 7
- Prof. D: Slots 8, 7, 4
- Prof. A: Slots 4, 1
What is the earliest slot when all can attend?
Step-by-step solution:
1. Find intersection of availability:
Prof. E: [6, 7]
∩ Prof. C: [3, 5, 6, 8]
∩ Prof. B: [4, 7]
∩ Prof. D: [4, 7, 8]
∩ Prof. A: [1, 4]
= ∅ (No common slots)
Answer: No common slot available
1. Find intersection of availability:
Prof. E: [6, 7]
∩ Prof. C: [3, 5, 6, 8]
∩ Prof. B: [4, 7]
∩ Prof. D: [4, 7, 8]
∩ Prof. A: [1, 4]
= ∅ (No common slots)
Answer: No common slot available