## 80-110 The Nature of Mathematical Reasoning

**Spring 2001**

*Dirk Schlimm*
# Homework No.9

Thursday, March 22, 2001

Due Tuesday, April 3, 2001

**1. Logical equivalence** (1 point)
Read FOL, pages 44-46 (Section 3.5). Do the following problem:

**2. Satisfiability and logical truth** (3 points)

Read FOL, pages 51-64 (Sections
3.7-3.8). Do the following problems:

- Page 55, Problem 18.
- Page 65, Problem 29.

(For an example of how the proof should look
like, consult the proof of "Small(c)" on page 61.)

**3. Alternative notation** (1 point)

Read FOL, pages 88-90 (Section
3.12). The "Polish notation" should remind you of the axiomatization
of sentential logic in Handout #16!

Do the following problem:

**4. Reflections** (5 points)

Imagine you ware at home over spring break and you met your older sister
who is a graduate student of physics at MIT. After you told her that
you are attending a course on the nature of mathematical reasoning,
she says: "Well, I know what the nature of mathematical reasoning
is - it's calculating. The Greeks started it 500 years ago with simple
equations, and now we have differential equations and computer
programs like Maple or Mathematica to solve them. It has become a
zillion times more complex, but basically it's still the same thing."
What would you reply to her? Write a few paragraphs.