Math 2000 Solutions 1

Fall 2001

Exercise 2 of the Prologue, was assigned! Solutions will vary.

Unit 1C

10. All pianists are musicians, so the pianist circle should be entirely inside the musician circle.

14. The Venn diagram consists of two overlapping circles. The X in the overlap region indicates that there really are some pilots who are women.

30. The Venn diagram reflects the facts that all oceans are salt water bodies, not all salt water bodies are oceans, and fresh water and salt water bodies are disjoint (mutually exclusive).

38.

44a.

b. 21 people read WP and WSJ; note we must include those who read all three newspapers.

c. 8 people read all three newspapers.

d. As discussed in class, if we interpret or to be the inclusive or, then we must count everyone who reads one or more of NYT, WSJ, or WP, which amounts to 128 people. If we interpret or to be the exclusive or, then we must count everyone who reads one, but not more than one, of NYT, WSJ, or WP, which amounts to 77 people.

e. We must look for people inside the NYT circle, but not inside the WP circle; there are 38 such people.

Unit 1E

6. When stripped of all the legal terms, the initiative says:

Shall we have an amendment that allows a candidate to declare voluntarily that s/he will not serve more than three terms as Representative or two terms as Senator, but will not be penalized if s/he chooses not to make such a declaration?

a. The fact that the initiative is on the ballot implies that term limits are not currently mandatory.

b. No, if passed, the initiative would make term limits voluntary.

c. No, if passed, there would be no penalty for refusing to accept term limits.

8. Note that your current rate is equal to the new weekday nighttime rate. So you need estimates of the number of minutes you spend calling during the weekday daytime and during the weekend. The weekday daytime rate is five times the weekend rate. It turns out that if the number of weekday daytime minutes is less than one-third the number of weekend minutes, then the new plan is better. You might also want to ask about hidden service charges, taxes, or fees to connect the new service.