80-110 The Nature of Mathematical Reasoning
Homework No. 12
Monday, July 31, 2000
Due Wednesday, August 2, 2000
Since this homework is more technical than
usual, you are allowed and encouraged to work on it in small groups
(of two or three) and hand in one homework together. However, do not just split
the work into equal parts, but discuss the problems together, so that
everybody understands them.
1. Read FOL, pages 91-103 (Sections
4.1-4.4). Do the following problems:
- Page 95, Problem 4.
Hand in your answers on
a disk (in PC/IBM format). Name your files exactly as it is specified
in the problem.
- Page 104, Problem 21.
An example for a similar proof is given on page 102 of FOL. Make sure
to understand this example before attempting to solve this problem.
2. Read FOL, page 112 (Section
3. Give a semantic and a syntactic proof
for each of the following valid steps
- Modus tollens: From "A implies B" and "not B" infer "not A".
- Strenghening the antecedent: From "B implies C" infer "(A and B)
- Weakening the consequent: From "A implies B" infer "A implies (B