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80-110 Nature of Mathematical Reasoning

Spring 2002

Dirk Schlimm

Homework 10 (A)

Wednesday, March 27

Due Monday, April 8

1. Conditionals and biconditionals (2 points)

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 file 4-4.sen (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.

Read FOL, page 112 (Section 4.7).

3. Validity (3 points)

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)".
4. First order logic (Here it comes!) (3points)

Read carefully FOL, pages 115-127 (Sections 5.1-5.8). Do the following problems:

• Page 119, Problem 1 (Filename: 5-1.sen).
• Page 124, Problem 6 (Filename: 5-6.wld).
• Page 125, Problem 10.
• Page 127, Problem 11 (Filename: 5-11.sen).
• Page 131, Problem 17.
5. Even more readings and questions (2 points)

Read FOL, pages 132-141 (Sections 5.9-5.10), and pages 152 (Section 5.13).

• Write up three questions from the readings assigned in this homework: either questions about something that you did not understand at all, or questions about what you think is most important. If you choose the latter, give also short answers.