1. Construct the truth table for each of the following expressions. Indicate for each expression whether it is a tautology, a contradiction, or neither (meaning that it is contingent).

a) (P (P Q)) Q

b) (P Q) (P Q)

c) (Q (P Q)) P

5. Reduce the expression Q ((P Q) P) to T. Your proof must use logical equivalences(not truth tables) and you must justify every step with the law (or laws) you use for the step.