Math 99 (Notes)

# Exam 1 Review Sheet:

For the exam on Friday, it would help you to do the following things:

1. Learn the definitions you needed to know for the quiz, plus the definition of a function. Know the definitions precisely. You should know the statements in formal language, as well as interpretations in words. E.g., "AÍB" means "("x)(xÎA Þ xÎB)" and this can be read as "everything in A is also in B".

2. Do "blank-paper practice" for the problems on the four problem sets that have been handed back. Note: You should be able to do all the problems, including the hard ones. Avoid repeating a mistake you made on the problem set.

3. Understand these challenging concepts:

1. Í vs. Î vs. =
2. AÍB vs. AÇB
3. P(A), the power set of A.
4. ("x)(P(x)) vs. { x | P(x) }
5. "For all x, ..." vs. "There exists an x where ..."
6. ("x)(\$y)(P(x,y)) vs. (\$y)("x)(P(x,y))
7. PÙQ vs. AÇB
8. P(x) Þ Q(x) vs. { x | P(x) and Q(x) }

4. Know the negations of the various types of propositions we've studied.

5. Know the contrapositive, converse, and inverse, and which ones are equivalent.

6. Know how to translate English into formal logic and vice versa.

7. Know how to use mathematical induction.

8. Know the proofs of these key examples. You should not memorize them, but should remember the central idea(s) and reconstruct the proof from that memorized core.

1. ØÍA for all A (theorem 9/26/01)
2. AÍB if, and only if, P(A)ÍP(B) (theorem 10/1/01)
3. A´B=Ø if, and only if, A=Ø or B=Ø (PS4#4)
4. For A¹Ø and B¹Ø, A´BÍC´D iff AÍC and BÍD (PS4#6)

 Math 99 (Fall 2001) web pages Created: 28 Apr 1999 Last modified: 05 Oct 2001 18:14:35 Comments to: `dpvc@union.edu`