$(5$ marks$)$ In class, we discussed the fact that the following language is known to be decidable.

$A_{\text{D}\text{F}\text{A}}=\{($:$M,w$:$)|Mis$ a DFA, $wis$ a string, and $M$ accepts $w\}$

$($In other words, there exists an algorithm that can take any DFA $M$ and any string $w$ as input

and can always correctly answer the question of whether or not $M$ accepts $w.)$

Consider the language is a DFA, and $M$ accepts at least one string

xin$\{0,1{\}}^{**}$ that has a length of $3$