Prove that any finite set of words is regular. How many states is sufficient for a single word $w_1...w_m$? DFA
Prove that any finite set of words is regular. How many states is sufficient for a single word $w_1...w_m$?
For part 2, wouldn't it require M states if the word length is M?

A language over the alphabet $\Sigma$ will be a regular language given that it follows the following clauses: 


*

*$\epsilon$, {$a$} for $a\in\Sigma$.

*If $L_1$ and $L_2$ are regular languages, then $L_1\cup L_2$, $L_1L_2$, and $L^*$ are also regular.

*$L$ is not a regular language unless taken from those two clauses. 


A finite set of words taken from some alphabet will clearly be a regular language. As for the second part, you need $m+1$ states (hint: there is a tiny element in the first clause that should give you the reason to this). 
