2. Do the following proofs deductively. Justify each step in your proof with a law or inference rule.

a) If P Q, R Q, and P then prove R.

b) If P (Q R) and R Q then prove P.

5. Given the following premises:

if cows fly then there is a man in the moon

if there is a man in the moon then the earth is flat

cows fly

Prove the following conclusion:

the earth is flat.

Justify each step in your proof with a law or an inference rule.

6. For each of the following arguments, indicate which of the rules of inference are used (Modus ponens, Disjunctive syllogism, etc.).

a) If Mr. Smith or Mrs. Smith earns more than $30,000 per year, the Smith family can afford holidays in Hawaii. Since I know that either Mr. Smith or his wife earns more than $30,000, I conclude that the family can afford a holiday in Hawaii.

b) If John was at the party yesterday, he will sleep in. John did not sleep in. Consequently, he was not at the party.

c) If Susan studies hard, shell get an A and if she gets an A, shell be happy. Hence, if Susan studies hard, then shell be happy.