III. (10 points each) Problems
Do any three of the following four problems. If you do all four, I'll count your best three.
1) Use a truth table to determine if $\neg p \lor (q \rightarrow r)$ is logically equivalent to $r \lor \neg (p \rightarrow q)$.
2) Express the following argument in symbolic form and show, by applying rules of inference, that the argument is valid. Give the reason for each step in your proof.
If Ralph goes to graduate school, then he will be a professor. If Ralph doesn't go to graduate school, he will have to get a real job. If Ralph gets a real job, he will need a new suit. So, if Ralph doesn't become a professor, then he will need a new suit.