Homework 1

  1. Consider the defining relations of Rock-Scissors-Paper

      rsp_win = {(rock, scissors),
                 (scissors, paper),
                 (paper, rock)}
      rsp_tie = {(rock, rock),
                 (scissors, scissors),
                 (paper, paper)}

    What should the formal domain and range of these relations be?

    For each of these relations, indicate whether they are

    a. reflexive b. transitive c. a surjective function d. an injective function e. a permutation

    What would be the easiest way to write rsp_lose?

  2. Consider the natural relation between an amount between $0.00 and $1.00 inclusive and the sets of coins that can be made to give change in that amount. [Note that you have to be careful (as we have been before) to not make the change be e.g. P {1, 5, 10, 25} because duplicates.]

    Define the relation in Z, as best you can. Is the relation a function? If so, is it a total function?