1. Using a sequence of logical equivalences, demonstrate that (p q) is logically equivalent to p q. You may NOT use Table IV Line (e) or Line (f) in your sequence. Fair Warning: This problem will probably take you quite a while to work through! Hint: Create sequences of logically equivalent expressions starting from both expressions, and look for a time when your two sequences can meet in the middle. That is, lets say you need to show that A E. You can show that A B C, and that E D C, and then combine them to show that A E.

2. Using reasoning, demonstrate that (p q) (p r) is logically equivalent to p (q r). (Yes, we know that this is Table III Line (o) on the PoLE. No, you cant use that line as part of your reasoning.)