Let L₁ be the language represented by the regular expression b^*ab^*(ab^*ab^*)^* and L₂ = { w ∈ (a + b)^* | |w| ≤ 4 }, where |w| denotes the length of string w. The number of strings in L₂ which are also in L₁ is __________.

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 ___________.