$(1)$ Create a DFA called M$\_1$ that recognizes the d lang of strings of $**\{a{\}}^{\text{'}}s$ and $**\{b\}\text{'}$s having a length of exactly $2.\frac{1}{?}$

$(2)$ Show a logical analysis of the states in M$\_1.$

$\frac{\frac{?}{?}}{?}$

$(3)$ Create a DFA called M$\_2$ that recognizes the language of $**\{a{\}}^{\text{'}}s$ and $**\{\frac{?}{\text{b}\text{a}\text{r}}(b)\}\text{'}$s that contains zero or more $**\{a{\}}^{\text{'}}s$ afollwed by one or more $**\{b{\}}^{\text{'}}s.\frac{1}{?}$

$(4)$ Show a logical analysis of the states in M$\_2.$

$(5)$ Use the $!\{$algorithm from class$\}$ to write lgraf code for a DFA called $M$ that recognizes the @lang L$($M$\_1)\backslash$u L$($M$\_2).$

$/1$

$(6)$ Show a logical analysis of the states in M$.$