## Homework 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`

?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?