Part $3$: Pangrammatic Strings

A string over the alphabet $$ is said to be pangrammatic if it contains at least one occurrence of

each letter. Some examples of pangrammatic strings over the English alphabet include "a wizard's

job is to vex chumps quickly in a fog" and "pack my box with five dozen liquor jugs" $($spaces

added for comprehension$).$ Prove that for any alphabet $,$ the language PanGram$()$ of pan$-$

grammatic strings over $$ is regular. In particular, you should describe how to construct a DFA for

PanGRam$()($with some combination of a clear English description, careful mathematical nota$-$

tion, and pseudocode$).$ You do not need to prove that this DFA is correct with the rigor of Part $2$

on this homework.

Careful: It is not enough to demonstrate that PanGram$()$ is regular for one choice of $$ : you

should instead describe a method that will produce a correct DFA for any $.$