(b) In this question, we consider CFGs in which we take S to be the initial variable. For each of the following statements, state whether they are true or false. Correct answers are awarded 4 marks; wrong answers are penalised by 1 mark (to a minimum of O marks for this question). Omitted answers do not contribute positively or negatively to your grade. [16 marks] i. The CFG over the alphabet {a,b,=, +, 1,; } with reductions S +A;S|A a=E|A+b=E E + E +6E+1E+V+V True or false: the language of this CFG is infinite (meaning: contains infinitely many strings). ii. The CFG over the alphabet {(x)} with reductions S +(5) | S + (SS) | S +() True or false: the language of this CFG is precisely the set of non-empty strings over {()} with balanced brackets, including e.g. (),(0), (000)),... iii. The CFG over the alphabet {()} with reductions $+(1) | S +T(T) | S +(T((T)T)) | Sne | T +S True or false: the language of this CFG is precisely the set of (possibly empty) strings over {(,)} with balanced brackets, including e.g. 0, 0), (000)),.... iv. The CFG over the alphabet {a,!} with reductions S + HSHS S AH!! S + | H+SHS True or false: the CFG is left-recursive