Exam I will be in the usual classroom on Friday, September 16, 2005. It will cover the material up through methods of proof, but not the material on sets that we started on Friday the 9th.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with.

The exam will have problems similar to those on the homework, and questions related to the lectures. Fifty minutes is not very long for an exam, but you should be able to finish without rushing, provided that you give brief, clear answers without unnecessary explanation. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

The main topics are quantified statements and their negations, and basic methods of proof. The following will definitely be covered, although the exam not necessarily limited to these topics:

1.	Logic notation, connectives, and tautologies.
2.	Using a truth table to analyze a compound statement.
3.	Existentially and universally quantified statements, and multiply quantified statements. Converting between quantified statements given in words and in mathematical notation.
4.	Negation of quantified statements.
5.	Proving implications by direct proof.
6.	Proving or disproving quantified statements.
7.	Proof by contradiction: what it is, why it works, using it to prove statements.

One should be familiar with the standard notations ( N, Z, Q, R, C ) that we used for the sets of natural numbers, integers, rational numbers, real numbers, and complex numbers.

You do not need to memorize tautologies, although you should be familiar with the common ones that we used in class such as DeMorgan's laws. It is not important to be able to verify tautologies by manipulating equivalent statements. You do not need to master the ways to deal with proving compound implications such as P => ( Q or R ). Focus on the three basic proof situations ( in 5, 6, and 7 above ), and on how to approach them in examples such as those we did in class and those that appear on the homework.

The following do not appear on this exam: interpretation of quantified statements using “truth sets,”, Archimedean Property of the real numbers, Triangle Inequality, the book's “rules of inference,” or the book's “vacuously true” statements (which we will talk about later, when we need them).