$>|>$ Create a $\backslash$graf document with your answers to the following problems.

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

$//$

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

II

$(3)$ Create a DFA called M$\_2$ that recognizes the language of $*\{$a$\}$s and $*\{$b$\}$s that contains zero or more $*\{$a$\}$s @fllwed by one or more $*\{$b$\}$s$.$

$/1$

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

$/1$

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

$/$l

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

$/1$

$(*)$ Two DFAs M$\_1$ and M$\_2$ are said yo be $!\{$equivalent$\}($written M$\_1=$M$\_2)$ if $L(M_1)=L(M_2).$