Summer 2000

Dirk Schlimm

# Homework No. 12

Monday, July 31, 2000
Due Wednesday, August 2, 2000

Note: 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 4.7).

3.  Give a semantic and a syntactic proof for each of the following valid steps of reasoning:

• Modus tollens: From "A implies B" and "not B" infer "not A".
• Strenghening the antecedent: From "B implies C" infer "(A and B) implies C".
• Weakening the consequent: From "A implies B" infer "A implies (B or C)".