Up: Math 99 Selected Course Notes
Exam 1 Review Sheet:
For the exam on Wednesday, it would help you to do the following things:
- Learn the definitions you needed to know for the quiz. Know the
definitions precisely. You should know the statements in formal language,
as well as interpretations in words. E.g., "A Í B" means "("x)(xÎA Þ xÎB)" and this can be read as "everything in
A is also in B".
- 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.
- Understand these challenging concepts:
- Í vs. Î vs. =
- P(A), the power set of A.
- ("x)(P(x)) vs. { x | P(x) }
- "For all x, ..." vs. "There exists an x where ..."
- ("x)($y)(P(x,y)) vs. ($y)("x)(P(x,y))
- PÙQ vs. AÇB
- P(x) Þ Q(x) vs. { x | P(x) and Q(x) }
- Know the negations of the various types of propositions we've studied.
- Know the contrapositive, converse, and inverse, and which ones are equivalent.
- Know how to translate English into formal logic and vice versa.
- 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.
- if A is a subset of B and B is a subset of C
then A is a subset of C (theorem 3.5)
- The various distributive laws (theorem 3.8 and PS4#2).
- Ø ´ A = Ø for all
A (theorem 3.11)
- A is a subset of B iff P(A) is a subset of
P(B) (theorem 3.14)
- For A != Ø and B != Ø, A x B
is a subset of C x D iff A is a subset of C and
B is a subset of D (PS4#5)
Up: Math 99 Selected Course Notes
Comments to:
dpvc@union.edu
Created: 28 Apr 1999 ---
Last modified: Aug 27, 1999 10:22:58 AM