5. (5 points) Use a truth table to show the following equivalence: ~(~pg)^(pVq) =P 6. Dumpulus is dishing out gossip about himself and his friends Abforsoft, Bloronski, and Crafloniae. He tells you that, among this group of four, Dumpulus knows all three of the others, Abforsoft knows exactly 2 of the others, Bloronski knows exactly 2 of the others, and Crafloniae knows exactly 2 of the others. (Assume that if Person in knows Person n, then Person n knows Person m, and we won't count a person knowing themself as something worth mentioning.) Dumpulus is a BIG OL LIAR!!! How do we know that what Dumpulus is saying is not true? (Hint: Think graph theory.) 8. Without using any theorems from the book, prove the following statement: The sum of any two odd numbers is even.