Problem $4($Finite languages are regular$)$

$10$ Points

Show that if $L$ is any language containing a finite number of strings $($i$.$e$.,|L|$ is finite$)$ then $L$

is regular. Do so by describing a general procedure that takes any such finite language $L$ and

shows how to construct a DFA that recognizes $L($do not rely on NFAs or regular expressions$).$ To

illustrate that your general procedure works, give an example of what DFA it would produce if you

started with the language $L=\{00,01,010\}.$