Consider the DFA over the alphabet $\{0,1,2\}$ defined as follows:

q$0$ is start state; $\{$q$0,$ q$2\}$ are accepting states.

$($q$0,0)->$q$1$

$($q$0,1)->$q$0$

$($q$0,2)->$q$2$

$($q$1,1)->$q$0$

$($q$1,0)->$q$3$

$($q$1,2)->$q$3$

$($q$2,0)->$q$0$

$($q$2,1)->$q$0$

$($q$2,2)->$q$2$

$($q$3,0)->$q$3$

$($q$3,1)->$q$3$

$($q$3,2)->$q$3$

From the following, select the language matched by this DFA. $($in all possible answers, w refers to a string that belongs to the said language$)$

Question $2$Answer

a$.$

L contains all w such that every $2$ in w is immediately followed by a $0,$ or is immediately preceded by a $1$

b$.$

L contains all w such that every $2$ in w is immediately followed by a $1,$ or is immediately preceded by a $0$

c$.$

L contains all w such that no $0$ in w is immediately followed by a $1,$ or is immediately preceded by a $2$

d$.$

L contains all w such that every $0$ in w is immediately followed by a $1,$ or is immediately preceded by a $2$