Math 39 Homework #5 When I was young I observed that nine out of every ten things I did were failures, so I did ten times more work. George Bernard Shaw

	Reading Read what we will cover in the next class: 2.2. When reading 2.2 pay special attention to the following concepts: extension of a formal system, consistent extension, complete extension, the Adequacy Theorem, decidable, and the many propostions that arise in this section.

	Problems The following problems are due by the beginning of class on Wednesday 10/7. 2.1: 3a,d. 2.2: 6, but just for axiom L2. Let M = {p,q} be a model. Which of the following wfs are satisfied by M? r p p -> s ~~~r (~p -> r) -> (s -> q) For each of the following wfs, specify a model which satisfies the wf. r p p -> s p -> p (~p -> r) -> (s -> q) Rewrite the proof of Lemma 2 from class (Proposition 1.9 in the book) using the notions of model and satisfaction rather than the notion of valuation which we used in class. We say that a wf A is satisfiable iff A has at least one model and that A is a tautology iff A is satisfied by all models. Prove that a wf A is satisfiable iff ~A is not a tautology.