York University

CSC 2001

1. Question 1–Sets and functions Let n1, n2, . . . , n9 denote the 9 digits of you Student ID. We also let Σ = {a, b, c, . . . x, y, z} be our standard alphabet of letters. We define the following three subsets of the natural numbers: A = {n1, n2, . . . , n9} B = {n1, n2, n3, n4, n5} C = {n6, n7, n8, n9} And we define one subset of Σ: D = {σ ∈ Σ | σ occurs as a letter in your (first last or middle) name} (a) Spell out all of the above four sets by listing their elements. What are the sizes of the sets A, B, C and D? (b) Does there exist a function f that is one-to-one from A to D? If so define one, if not, explain why not. (c) Does there exist a function g that is onto from A to D? If so define one, if not, explain why not. (d) How many