The language $$\left\{ {{a^m}{b^n}{c^{m + n}}\left| {m,n \ge } \right.} \right\}$$ is

Consider the following grammar $$G:$$
$$\eqalign{ & S \to bS\,\left| {\,aA\,\left| {\,b} \right.} \right. \cr & A \to bA\,\left| {\,aB} \right. \cr & B \to bB\,\left| {\,aS\,\left| {\,a} \right.} \right. \cr} $$

Let $${N_a}\left( w \right)$$ and $${N_b}\left( w \right)$$ denote the number of $$a's$$ and $$b's$$ in a string $$w$$ respectively. The language
$$L\left( G \right)\,\,\, \subseteq \left\{ {a,b} \right\} + $$ generated by $$G$$ is

Consider the following decision problems:
$${P_1}$$ Does a given finite state machine accept a given string
$${P_2}$$ Does a given context free grammar generate an infinite number of stings.

Which of the following statements is true?

If $${L_1}$$ is a context free language and $${L_2}$$ is a regular which of the following is/are false?