Math 39 Homework #6 My mind rebels at stagnation. Give me problems, give me work, give me the most obstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere. Sherlock Holmes

	Reading Read what we will cover in the next class: 2.2, 3.1. When reading 2.2 pay special attention to the following concepts: complete extension, the Adequacy Theorem, decidable, and the many propostions that arise in this section. When reading 3.1 pay special attention to the following concepts: predicates, universal quantifier, existential quantifier, bound variables, the relationship between the existential and the universal quantifier.

	Problems The following problems are due by the beginning of class on Friday 10/9. 2.2: 7, 9, 10. (Note: Soundness and Completeness may be helpful). Prove that if F is an extension of L, then F U {A} is inconsistent iff F |- ~A (i.e., F deduces ~A). Prove that if F is a consistent extension of L and A is a wf, then F U {A} or F U {~A} is consistent. Give an example to justify that this is an inclusive-or.