Let $=\{0,1\}$ and let $F$ be the language of all strings over $$ of length exactly $5.$

$($a$)(3$ points$)$ Find an NFA with $6$ states that recognizes $D.($No need to prove that it is

correct.$)$

$($b$)(7$ points$)$ Show that there is no NFA with $5$ or fewer states that recognizes $D.$

HINT: assuming that there is such an NFA, how many states are listed in an accepting

path for $11111?$