Let A be the language consisting of all strings over the alphabet $\{$a$,$ b$,$ c$\}$ that

are alphabetically sorted, i$.$e$.,$ all a$$s are to the left of all b$$s$,$ and all b$$s are to the left of all

c$$s$.$ Note that the empty string $\backslash$epsi is in A$.$ Also, strings in A may have no a$$s or no b$$s or no

c$$s$.$

$$ Construct a DFA with five states that accepts the language A$.$ As always, justify your

answer.

$$ Construct an NFA with three states that accepts the language A$.$ As always, justify

your answer.