Math 89 Winter 2012

Set Theory - Homework

Set Theory - Homework

Main page | Syllabus |
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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 | |
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Fri 6 Jan | Discussion 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 Jan | Discussion for today: Justify that the inverse of a relation exists. |

Weds 11 Jan | Discussion 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 Jan | Written Homework: Chapter 3 Exercises 2.8 (p. 46), 3.5, 3.6 (p. 52) (due Wed 18 Jan) |

Week 3 | |

Weds 18 Jan | Written Homework: Chapter 3 Exercise 4.7 (p. 54) (due Wed 25 Jan) Interpret "usual laws" as a ^{n}b^{n} = (ab)^{n} and a^{n}a^{m} = a^{n+m}. |

Fri 20 Jan | Written Homework: Chapter 3 Exercises 5.15, 5.16 (p. 63) (due Wed 25 Jan) |

Week 4 | |

Mon 23 Jan | Discussion for today: Chapter 4 Exercise 1.5 (p. 68). Written Homework: Chapter 4 Exercise 2.4 (p. 73) (due Wed Feb 1) |

Weds 25 Jan | Written Homework: Chapter 4 Exercises 3.8, 3.11 (p. 79), 4.7 (p. 85) (due Wed Feb 1) |

Fri 27 Jan | Discussion 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 Feb | Midterm 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 Feb | Written Homework: Chapter 6 Exercises 3.2 (p. 114), 5.5, 5.12 (p. 123) (due Wed Feb 15) |

Weds 8 Feb | Midterm I due. |

Week 7 | |

Mon 13 Feb | Written homework: Chapter 7 Exercises 1.1, 1.4, 1.6 (p. 132) (due Wed Feb 22) |

Weds 15 Feb | Discussion 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 Feb | Discussion for today: Exercise 2.4 in Chapter 9 (p. 164). |

Weds 22 Feb | |

Fri 24 Feb | |

Week 9 | |

Mon 27 Feb | Midterm II distributed. |

Weds 29 Feb | |

Fri 2 Mar | |

Week 10 | |

Mon 5 Mar | Midterm II due. |

Weds 7 Mar | Presentations. |

Last modified 2 Mar 2012.