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Consider n activities in the activity selection problem a1, a2, a3,…,an. For activity ai, let si be the starting time and fi be the finishing time. Then two activities ai and aj are compatible when;
  • a)
    [si, fi) ꓵ [sj, fj) = φ
  • b)
    [si, fi) ꓴ [sj, fj) = φ
  • c)
    [si, fi) > [sj, fj)
  • d)
    [si, fi) ≠ [sj, fj)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider n activities in the activity selection problem a1, a2, a3,&he...
The duration of one activity should not partly or completely overlap with the duration of another activity. Their intersection should be null.
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Consider n activities in the activity selection problem a1, a2, a3,&he...
Compatible Activities in Activity Selection Problem:
Activity selection problem involves selecting a maximum number of compatible activities that can be performed concurrently. Two activities ai and aj are considered compatible if their time intervals do not overlap.

Explanation:

a) [si, fi) ∩ [sj, fj) = ∅:
This condition states that the time intervals of activities ai and aj do not overlap. In other words, the finishing time of activity ai is before the starting time of activity aj or vice versa.
For example, if activity ai has starting time si = 1 and finishing time fi = 4, and activity aj has starting time sj = 5 and finishing time fj = 7, then these two activities are compatible because their time intervals do not overlap.
Therefore, option 'a' is the correct answer as it represents the definition of compatibility in the activity selection problem.
By satisfying this condition, we can ensure that the selected activities do not conflict with each other in terms of time and can be performed concurrently.
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Consider n activities in the activity selection problem a1, a2, a3,…,an. For activity ai, let si be the starting time and fi be the finishing time. Then two activities ai and aj are compatible when;a)[si, fi) ꓵ [sj, fj) = φb)[si, fi) ꓴ [sj, fj) = φc)[si, fi) > [sj, fj)d)[si, fi) ≠ [sj, fj)Correct answer is option 'A'. Can you explain this answer?
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