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Given a set of arbitrary class schedules X and a person P. Find all the possibilities that P can take in a day. If P can take a class in X they must

Example:
Class 1 8:00 - 9:00
Class 2 10:00 - 11:15
Class 3 11:00-12:30
Class 4 1:00 - 2:30

Answer: Person P can take classes [1,2,4], and [1,3,4]

Given a set of random intervals, merge the overlapping intervals.

For example:
Intervals: [(1,4), (2,5), (6,8), (8, 12), (9, 11)]
Result: [(1,5), (6,12)]

Given a an interval A and a set of non unique intervals B and arbitrary integer X,

Return an interval "C" That is the interval or intervals resulting from subtracting from A the intervals that are repeated in B at least X times

For example inputs:
A=1-100
B=[1-50,1-50,1-50,70-100, 80-90]
X=3

Your output would be:
C=51-100