Math 199 (Assignments)

1. [To be turned in on Monday]

   In class, we looked at diagrams for the statement "Everybody loves somebody". An arrow from one person to another means the first loves the second, and no arrow means the first doesn't love the second.

   Consider the situation for four people: Alan, Betty, Charles, and Debbie.

   For the statements below, produce several example diagrams (when possible) that satisfy each. Your selection of examples should give some sense of the breadth of possibilites. (For instance, what is the diagram with the fewest arrows? What is the one with the most? What is a typical example?)

   Describe each of the statements in terms of the kinds of arrows that they require. Be as precise as you can about exactly what conditions must be met. (Any diagram that satisfies your conditions should make the statment true, and any diagram that makes the statement true should satisfy your conditions.)

   If any of these are ambiguous, describe the two (or more) possible meanings, and give examples of diagrams that distinguish the two (that is, where one is true but not the other).

   Do any of the statements imply any of the others? (A statement implies another if the first being true requires the second to be true.)

   1. Everybody loves everybody
   2. Nobody loves everybody
   3. Everybody loves nobody
   4. Nobody loves nobody
   5. Nobody loves somebody
   6. Somebody loves everybody

Math 199 (Fall 2019) web pages Created: 13 Sep 2019 Last modified: 13 Sep 2019 at 7:42 PM Comments to: dpvc@union.edu

Assignments