Let n₁, n₂, . . . , n₉ denote the 9 digits of you Student ID. We also let = { 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 :

D = { | occurs as a letter in your (first last or middle) name}

1. Spell out all of the above four sets by listing their elements. What are the sizes of the sets A, B, C and D?
2. Does there exist a function f that is one-to-one from A to D? If so define one, if not, explain why not.
3. Does there exist a function g that is onto from A to D? If so define one, if not, explain why not.
4. How many elements are there in the set B C?
5. (e)Is is true that B C A²?
6. As a relation over N, is B X C reflexive, transitive and symmetric? For each property explain why or why not.