Let *L _{1}* be the language represented by the regular expression

*b*and

^{*}ab^{*}(ab^{*}ab^{*})^{*}*L*, where |w| denotes the length of string

_{2}= { w ∈ (a + b)^{*}| |w| ≤ 4 }*w*. The number of strings in

*L*which are also in

_{2}*L*is __________.

_{1}Consider the 5-state DFA $M$ accepting the language $L(M) \subseteq (0+1)^*$ shown below. For any string $w \in (0+1)^*$ let $n_0(w)$ be the number of 0's in $w$ and $n_1(w)$ be the number of 1's in $w$.

Which of the following statements is/are FALSE?

Consider the following two regular expressions over the alphabet {0,1}:

$$r = 0^* + 1^*$$

$$s = 01^* + 10^*$$

The total number of strings of length less than or equal to 5, which are neither in *r* nor in *s*, is ________

Consider the language L over the alphabet {0, 1}, given below:

$$L = \{ w \in {\{ 0,1\} ^ * }|w$$ does not contain three or more consecutive $$1's\} $$.

The minimum number of states in a Deterministic Finite-State Automaton (DFA) for L is ___________.