Consider the following two statements about regular languages:

S₁: Every infinite regular language contains an undecidable language as a subset.

S₂: Every finite language is regular.

Which one of the following choices is correct?

Consider the following language.

L = { w ∈ {0, 1}* | w ends with the substring 011}

Which one of the following deterministic finite automata accepts L?

Consider the following language.

L = {x $$ \in $$ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3}

The minimum number of states in a DFA that accepts L is ______.

Let $\Sigma$ be the set of all bijections from $\{1, \ldots, 5\}$ to $\{1, \ldots, 5\}$, where id denotes the identity function, i.e. $\operatorname{id}(j)=j, \forall j$. Let $\circ$ denote composition on functions. For a string $x=$ $x_1 x_2 \cdots x_n \in \Sigma^n, n \geq 0$, let $\pi(x)=x_1 \circ x_2 \circ \cdots \circ x_n$. Consider the language $L=\left\{x \in \Sigma^* \mid \pi(x)=i d\right\}$. The minimum number of states in any DFA accepting $L$ is $\qquad$