$($II$)$ Given the alphabet as $\{0,1\},$ write a DFA for the following three regular languages.

$($Give the complete description of the DFA, and also as a transition graph$)$

$($i$)$ L $=\{$w $|$ w is a string of even length$\}$

$($ii$)$ L $=\{$w $||$w$|$ mod $3=0\}$

$($iii$)$ L $=\{$w $|$ w contains the string $001$ as a substring$\}$

$($iv$)$ L $=\{$w $|$ w does not contain two consecutive $1\text{'}$s$\}$

$($III$)$Choose any DFA made in Problem $($II$),$ describe the extended transition function on a string recursively using transitions one symbol at a time of following problems:

$($i$)$ A string $($of length $>=4)$ that belongs to the language

$($ii$)$ A string $($of length $>=4)$ that does not belong to the language