[Note for Mac users] |

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., "
" means "*A*Í*B*(" " and this can be read as "everything in*x*)(*x*Î*A*Þ*x*Î*B*)*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*)) *P*Ù*Q*vs.*A*Ç*B* vs.*P*(*x*) Þ*Q*(*x*){ *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)

- if

Comments to: dpvc@union.edu

Created: 28 Apr 1999 --- Last modified: Aug 27, 1999 10:22:58 AM