## Assignments for Weeks 2 and 3

### Reading

Read Chapter 2 (logic for Week 2, incidence geometry for Week 3).
Deemphasize (but do not ignore!) projective and affine geometry (pp.
81-90).

The extra logic questions below come from my logic notes for
Math. 302, and I will draw on them for lectures, too.
The notes probably tell you more about logic than you really want
to know this week, but here they are:

### Discussion questions

- Express in logical notation (quantifiers and
connectives, plus a bare minimum of English):
- Everybody loves a lover.
(Define "lover" in the sort of way we defined an
integer to be a "square".)
- All that glitters is not gold.
- Every U.S. citizen, and any person who earns
income in the United States, must file a tax return.
- Taxpayer Smith may claim his daughter as a dependent,
provided that she is not married and filing a joint return,
if he provides more than half of her support,
or if he and another person together provide more than half of her
support and he paid over 10% of her support.
(To avoid lengthy initial quantifiers and conditions, let S = Smith, D =
daughter, and treat these as names, not variables.)

- Translate into standard mathematical English:
[Click here.]
- Exercise 6, p. 92: Proposition 2.3 (see p. 71).

### Homework due Wednesday, Sept. 20 (in Week 4)

** There are two W questions this time (because we covered two
subjects, and because the first question is short).
**
- Express in logical notation (quantifiers and
connectives):
- n is an even number.
- For every number that is a perfect cube, there is a
larger number that is even.

- Translate into standard mathematical English:
[Click here.]
(A really good answer uses no letters for variables and is brief.)
**(W)**
- Exercise 1, p. 91.
- Exercise 2, p. 91.
- Exercise 4, p. 92.
- Exercise 5, p. 92.
- Exercise 6, p. 92
(Propositions 2.4 and 2.5 only)
**(W)** (See p. 71 for the
statements of the propositions.)

**Use and incorporate the hint provided in lecture.
**
- Exercise 9, pp. 92-93. (Part (c) is especially important.)