Question $4-$Languages, DFAs and NFAs

lPease create a random Id that start with $22$ or $21$ and do it for me

Let $n_1,n_2,$dots,$n_9$ denote the $9$ digits of you Student ID$.$ We let $=\{0,1,2,3,4,5,6,7,8,9\}$

be the alphabet of digits. Your student ID is a word over this alphabet. We define the

following languages:

$A=\{n_1{n}_{2}dots{n}_9\}$

$B=\{w|wis$ a student $IDof$ some student $in$ this class $\}$

The language A contains only one word, namely your student ID$.$ The language $B$

contains exactly all student IDs of students in sections A and B of this class. Note

that all student IDs of students enrolled in this class have the prefix $\text{'}21\text{'}$ or the prefix

$\text{'}{22}^{\text{'}}$

Please create a random Id and do it for me

$($a$)$ Is your student ID accepted by the following NFA? Explain why or why not:

$($b$)$ Show that A and $B$ are regular languages.

$($c$)$ Design a DFA that accepts all $9-$digit words over $$ that have the prefix $\text{'}21\text{'}$ or the

prefix $\text{'}{22}^{\text{'}}$ and rejects all words without these prefixes, as well as all words that

have a different length. $($You may provide a state diagram or a formal description$).$

$($d$)$ Identify the language that the NFA from part $($a$)$ recognizes.