Consider the $$NFA$$ $$M$$ shown below.

Let the language accepted by $$M$$ be $$L.$$ Let $${L_1}$$ be the language accepted by the $$NFA$$, $${M_1}$$ obtained by changing the accepting state of $$M$$ to a non accepting state and by changing the non accepting state of $$M$$ to accepting states. Which of the following statements is true?

The Finite state machine described by the following state diagram with $$A$$ as starting state, where an arc label is $$x/y$$ and $$x$$ stands for $$1-bit$$ input and $$y$$ stands for $$2$$-bit output

The smallest finite automaton which accepts the language
$$L = \left. {\left\{ x \right.} \right|$$ length of $$x$$ is divisible by $$\left. 3 \right\}$$ has

Consider a $$DFA$$ over $$\sum { = \left\{ {a,\,\,b} \right\}} $$ accepting all strings which have number of $$a'$$s divisible by $$6$$ and number of $$b'$$s divisible by $$8$$. What is the minimum number of states that the $$DFA$$ will have?