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

1. 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.)
2. Translate into standard mathematical English: [Click here.]
3. 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).
1. 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.
2. Translate into standard mathematical English: [Click here.] (A really good answer uses no letters for variables and is brief.) (W)
3. Exercise 1, p. 91.
4. Exercise 2, p. 91.
5. Exercise 4, p. 92.
6. Exercise 5, p. 92.
7. 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.
8. Exercise 9, pp. 92-93. (Part (c) is especially important.)