Q$1(6$ points$)$

Question $1-$Designing NFAs

Let $n_1,n_2,n_3$ be the three smallest digits occuring in your student ID that are greater

than $1($that is$,$ greater or equal to $2)$ and all different. Eg$.$ if your student ID was

$183205720,$ then you'd have $n_1=2,n_2=3$ and $n_3=5.$ State clearly what your

numbers $n_1,n_2,n_3$ are. Let $=\{0,1\}$ be an alphabet.

$($a$)$ Design an NFA that accepts all words over $$ with a number of $0$ s that is divisible

by $n_1+n_2$ or a number of $1$ s that is divisible by $n_3.$

$($b$)$ Design an NFA that accepts all words over $$ that start with a number of $0$ s

divisible by $n_1,$ followed by a number of $1$ s divisible by $n_2,$ followed by exactly $n_3$

Please draw an automaton for this with no accept state and it should contain $5$ zeros and $4$ ones