Question $2.$

The symmetric difference of the languages $L1$ and $L2,$ denoted by $L1L2,$ is defined in the following way.

$L1L2=\{w$:$wisin$ exactly one $ofL1$ and $L2\}$

Let $=\{0,1\}.$ Consider the following languages over $.$

$A=\{w$ : the length $ofwis$ greater than $or$ equal $to3$ but less than $or$ equal $to5\}$

$B=\{w$ : the length $ofwis$ greater than $or$ equal $to2$ but less than $or$ equal $to4\}$

$C=\{w$ : the length $ofwis$ odd $\}$

$($a$)$ Give the state diagram for a DFA that recognizes A$.(2$ points$)$

$($b$)$ Give the state diagram for a DFA that recognizes B$.(2$ points$)$

$($c$)$ Give the state diagram for a DFA that recognizes $\frac{A}{{?}_{\frac{?}{?}}}B.(2$ points$)$

$($d$)$ If you use the construction from class to get a DFA for the language $(\frac{A}{{?}_{\frac{?}{?}}}B)C,$ how many states will it

have? $(1$ point$)$

$($e$)$ Give a $5-$state DFA that recognizes $(\frac{A}{{?}_{\frac{?}{?}}}B)C.(3$ points$)$