The language $$L = \left\{ {{0^i}{{21}^i}\,|\,i \ge 0} \right\}$$ over the alphabet $$\left\{ {0,1,2} \right\}$$ is

Consider the following statements about the context-free grammar
$$G = \left\{ {S \to SS,\,S \to ab,\,S \to ba,\,S \to \varepsilon } \right\}$$
$$1.$$ $$G$$ is ambiguous
$$2.$$ $$G$$ produces all strings with equal number of $$a's$$ and $$b's$$
$$3.$$ $$G$$ can be accepted by a deterministic $$PDA$$.

Which combination below expresses all the true statements about $$G?$$

Let $${N_f}$$ and $${N_p}$$ denote the classes of languages accepted by non-deterministic finite automata and non-deterministic push-down automata, respectively. Let $${D_f}$$ and $${D_p}$$ denote the classes of languages accepted by deterministic finite automata and deterministic push-down automata, respectively. Which one of the following is TRUE?

Consider the language :
$${L_1} = \left\{ {{a^n}{b^n}{c^m}\left| {n,m > 0} \right.} \right\}$$ and $${L_2} = \left\{ {{a^n}{b^m}{c^m}\left| {n,m > 0} \right.} \right\}$$

Which of the following statement is FALSE?