1. Discrete Mathematics
Label each relation as a function or not a function. Label each function as 1-1 or not 1-1. Label
each function as onto or not onto. (Circle as appropriate under each relation.) With domain Z and
codomain Z: R_1 = {(x, y) y = x^2} function/NOT a function onto/NOT onto onto/NOT onto
With domain Z^+ U {0} and codomain Z+ U {0}: R_2 = {(z,y) | function/NOT a function one-
to-one/NOT one-to-one With domain R and codomain R: Rz = {(x, y) | |t/| = x} function/NOT a
function one-to-one/NOT one-to-one onto/NOT onto With domain R and codomain R^+ u {0}:
= {(x, y) | y = |z|} function/NOT a function one-to-one/NOT one-to-one onto/NOT onto With
domain S = {Alice, Bob, Charlie, Dave, Eve) and codomain L = {Java, C++, Python, Scheme}
R_5 = {(Alice, Scheme), (Bob, Java), (Charlie, Python), (Dave, C++), (Eve, Java)}
function/NOT a function one-to-one/NOT one-to-one onto/NOT onto
Solution
1. Function , NOT one-to-one , NOT onto
2. Function , one-to-one , NOT onto
3. Function , NOT one-to-one , NOT onto
4. Function , NOT one-to-one , onto
5. Function , NOT one-to-one , onto