Math 39 Homework #4

Why, sometimes I've believed as many as six impossible things before breakfast.
Lewis Carroll

Quiz

Remember that we have a quiz on Monday 10/5 on Lectures 2 - 4.

Reading

Read what we will cover in the next class: 2.2.

When reading 2.2 pay special attention to the following concepts:

  • valuation, tautology, the Soundness Theorem, extension of a formal system, consistent extension, complete extension, the Adequacy Theorem, decidable, and the many propostions that arise in this section.
This particular section in the book is one that you should probably plan to read twice. The first time, read it at a "high" level, just noting the definitions, the statements of propositions, and the explanatory text; skip the proofs the first time through (except for the short proof of the Adequacy Theorem which explains why we are interested in the propositions that appear in this section). Make sure that this global picture is clear and then go back and read it a second time at a "deep" level to understand the proofs and the details behind the claims made in the section.

Problems

The following problems are due by the beginning of class on Monday 10/5.
  • 2.1: 1, 2a.
This set of problems involves deductions that should be fairly straightforward and within your abilities based on class and the examples in the book. We'll talk some more about deductions on Monday and the second half of the deduction homework set will show up on Monday. Also, we'll start class next time with any questions you have about deductions and/or the proof of the Deduction Theorem.