CSCE 235

Handout 9:

Additional Problems for Proofs in Propositional Logic

August 31, 2006

1. Prove the following, first directly and then by contradiction.

a. If , , , and , then .

b. If , , , and , then .

c. If , , and , then .

d. If and , then .

e. If and then .

f. If and then .

g. If , , and , then .

h. If , and, then .

2. Prove the following.

a.

b.

c.

d.

* Based on Grimaldi (2003) and old exercise problems.