Q42

MSQ2 marks

Consider a context-free grammar $\text{G}$ with the following $3$ rules.

S \rightarrow a S, S \rightarrow a S b S , S \rightarrow c

Let $w \in L(G)$ . Let $n_{a}(w), n_{b}(w), n_{c}(w)$ denote the number of times $a, b, c$ occur in $w$ , respectively. Which of the following statements is/are TRUE?

(A)

$n_{a}(w)>n_{b}(w)$

(B)

$n_{a}(w)>n_{c}(w)-2$

(C)

$n_{c}(w)=n_{b}(w)+1$

(D)

$n_{c}(w)=n_{b}(w) * 2$

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