Problem 3. (20 Points, 4 each) Consider a school with five classes: A, B, C, D, E. The courses can be scheduled in two periods, named 1 and 2. Each class needs to be scheduled in one of the two periods, but there are some caveats. Some subsets of courses can not be scheduled in the same period because some students need to take both classes. There will be ten variables, one for each course/period combination. For example, for class A, there are a1 and a2. If a1=True this means that class A is scheduled in period 1. 1 Write all your functions in the following parts in python. Each function should output True when the required condition is met. Note: Place all the functions in a single python file and make sure to name your python file ps3.py for the auto-grader to recognize and compile the file. Also, do not include any print statements or header documentation in the file. Use function names as required by each question.

a) Define a function a(a1, a2, b1, b2, c1, c2, d1, d2, e1, e2). Each of the five classes must be scheduled in either period 1 or period 2, but not both.

b) Define a function b(a1, a2, b1, b2). Class A and B cannot be scheduled in the same period.

c) Class B and E cannot be scheduled in the same period, or Class B and C cannot be scheduled in the same period.

d) Define a function d(a1, a2, c1, c2, e1, e2). The three classes A, E, and C cannot be scheduled in the same period.

e) Define a function e(a1, a2, d1, d2). Class A and D must be scheduled in the same period.