I need help answering part d) of this question from my textbook

I need help answering part d) of this question from my textbook...

Suppose a school has three periods (called 1, 2, and 3) during which a class can be scheduled.  For each class, there are three variables.  For example, for class A, there are X_A1, X_A2, X_A3.  Setting X_A2 = 1 represents scheduling class A during period 2. 

    a)  Give a Boolean expression that evaluates to 1 if and only if A is scheduled in at least one of the three periods.

              answer: (X_A1 + X_A2 + X_A3)

    b)  Give a Boolean expression that evaluates to 1 if and only if A is not scheduled in more than one period.

              answer: (X_A1X_A2)(X_A1X_A3)(X_A2X_A3)

    c)  Give a Boolean expression that evaluates to 1 if and only if A and B are not scheduled in the same period.

               answer: (X_A1X_B1)(X_A2X_B2)(X_A3X_B3)

    d)  The final Boolean expression representing the entire scheduling problem will be a product of many terms.  If there are n classes and m pairs of classes that can not be scheduled at the same time, then how many terms will be in the entire Boolean expression?

                                             I'm thinking like 2ⁿ + 2^m but that seems off...