1. Question 1-Sets and functions Let ni, N2, ..., ng denote the 9 digits of you Student ID. We also let S = {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, ..., ng} B= {n1, N2, N3, N4, n5} C = {n6, 17, 18, ng} And we define one subset of : D= {0 | o 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 elements are there in the set B x C? (e) Is is true that B x C C A?? (f) As a relation over N, is B x C reflexive, transitive and symmetric? For each property explain why or why not