Math 89 Winter 2012
Set Theory - Homework

Discussion questions below are for discussion on the day they are listed. Written homework is given on the day on which the relevant material was covered, with its due date in parentheses.

Week 1
Fri 6 JanDiscussion for today: Chapter 1 Exercise 3.3 (p. 12)

Written Homework: Chapter 1 Exercises 3.6, 3.7, 4.4, 4.6 (pp. 12 and 15) (due Mon 9 Jan)
Week 2
Mon 9 JanDiscussion for today: Justify that the inverse of a relation exists.
Weds 11 JanDiscussion for today: The membership relation by itself cannot be an ordering in most cases. The union of the membership and identity relations is a partial order; is it possible for this union to be a total ordering?

Written Homework: Chapter 2 Exercises 5.7, 5.9 (p. 38) (due Wed 18 Jan)
Fri 13 JanWritten Homework: Chapter 3 Exercises 2.8 (p. 46), 3.5, 3.6 (p. 52) (due Wed 18 Jan)
Week 3
Weds 18 JanWritten Homework: Chapter 3 Exercise 4.7 (p. 54) (due Wed 25 Jan)

Interpret "usual laws" as anbn = (ab)n and anam = an+m.
Fri 20 JanWritten Homework: Chapter 3 Exercises 5.15, 5.16 (p. 63) (due Wed 25 Jan)
Week 4
Mon 23 JanDiscussion for today: Chapter 4 Exercise 1.5 (p. 68).

Written Homework: Chapter 4 Exercise 2.4 (p. 73) (due Wed Feb 1)
Weds 25 JanWritten Homework: Chapter 4 Exercises 3.8, 3.11 (p. 79), 4.7 (p. 85) (due Wed Feb 1)
Fri 27 JanDiscussion for today: Where N and Q are the natural numbers and rational numbers, respectively, consider the lexicographic orderings on NxQ and QxN. Is either a well-order? Dense? With endpoints? Are they isomorphic?
Week 5
Mon 30 Jan[homework for next week will be replaced by midterm.]
Weds 1 FebMidterm I distributed.

Discussion for today: prove that the sum of n copies of k is nk and the product of n copies of k is k^n, where n is a natural number and k is any cardinal.
Fri 3 Feb
Week 6
Mon 6 FebWritten Homework: Chapter 6 Exercises 3.2 (p. 114), 5.5, 5.12 (p. 123) (due Wed Feb 15)
Weds 8 FebMidterm I due.
Week 7
Mon 13 FebWritten homework: Chapter 7 Exercises 1.1, 1.4, 1.6 (p. 132) (due Wed Feb 22)
Weds 15 FebDiscussion for today: Theorem 1.2 in Chp 8 (p. 139) and the paragraph that follows.

Written Homework: Chapter 8 Exercises 1.10, 1.17 (p. 144) (due Wed Feb 22)
Fri 17 Feb
Week 8
Mon 20 FebDiscussion for today: Exercise 2.4 in Chapter 9 (p. 164).
Weds 22 Feb
Fri 24 Feb
Week 9
Mon 27 FebMidterm II distributed.
Weds 29 Feb
Fri 2 Mar
Week 10
Mon 5 MarMidterm II due.
Weds 7 MarPresentations.