The correct option is C Either C or D
Using the three clues we get the following pairings:
P - B - Not April or May
Q - A - March
R - Not C or D - January
Put them together to get the following table.
ABCDEQP RMarchFebruary January
This leaves S and T to be teaching either C or D and either in April or May.
We do not know who teaches C or D (between S and T).
Hence Option (c) is correct.