Let n$1,$ n$2,...,$ n$9$ denote the $9$ digits of you Student ID$.$ We define the following three

subsets of the natural numbers:

A $=\{$n$1,$ n$2,...,$ n$9\}$

B $=\{$n$1,$ n$2,$ n$3,$ n$4,$ n$5\}$

C $=\{$n$6,$ n$7,$ n$8,$ n$9\}$

$($a$)$ State your student ID and define the above three sets for your ID by listing their

elements. What are the sizes of the sets A$,$ B and C$?$

$($b$)$ Does there exist a function f from B to C that is one$-$to$-$one? If so define one, if

not, explain why not.

$($c$)$ Does there exist a function g from B to C that is onto? If so define one, if not,

explain why not.

$1$

$($d$)$ How many elements are there in the set A$2$

$?$

$($e$)$ As a relation over A$,$ is B $\backslash$times C reflexive, transitive and symmetric? For each

property explain why or why not.