Exam 1 Review Sheet:

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

1. 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".

   
   

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. P(A), the power set of A.
   3. ("x)(P(x)) vs. { x | P(x) }
   4. "For all x, ..." vs. "There exists an x where ..."
   5. ("x)($y)(P(x,y)) vs. ($y)("x)(P(x,y))
   6. PÙQ vs. AÇB
   7. 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 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. if A is a subset of B and B is a subset of C then A is a subset of C (theorem 3.5)

   2. The various distributive laws (theorem 3.8 and PS4#2).

   3. Ø ´ A = Ø for all A (theorem 3.11)

   4. A is a subset of B iff P(A) is a subset of P(B) (theorem 3.14)

   5. 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)