Set Theory Exercises 2

  • You may work alone or in a group of up to 3 people and turn in 1 per group. Make copies of your work so that you are prepared to present any of the exercises after you turn it in.
    1. Choose 1 of Mendelson p. 6 #1a or 1b
    2. Mendelson p. 11 #3
    3. Let f:A → B be a function and C1,C2 &sube A. Prove that f(C1 &cap C2) &sube f(C1) &cap f(C2). In addition, give an example to show that equality fails. Finally, what assumption do we need to make about f - one-to-one, onto, or both - in order to ensure equality holds? Prove your answer.

    (Graduate Problem) In Munkres p. 14 #2, pick two parts to complete.