Please answer either True or False to each of the following statements. You must also provide a valid brief $($at most three sentences$)$ justification to explain each of your answers.

$(1)$ For the given language A$=\{$ akbk $|$ k $>=0\},$ then it has CFG$,$ G $=($V$,\backslash$Sigma $,$ R$,$ S$),$ which V $=\{$S$\},\backslash$Sigma $=\{$a$,$ b$\},$ start variable S$,$ and rules S $->$ aSb $|$ b$.$