Consider the following context-free grammar $G$, where $𝑆, 𝐴,$ and $B$…

GATE · 2025 · CS · Set 1 · Computer Science & IT

Consider the following context-free grammar $G$ , where $𝑆, 𝐴,$ and $B$ are the variables (non-terminals), $a$ and $b$ are the terminal symbols, $S$ is the start variable, and the rules of $G$ are described as:

$𝑆 → 𝑎𝑎𝐵 | 𝐴𝑏𝑏 \\ \\𝐴 → 𝑎 | 𝑎𝐴 \\ \\𝐵 → 𝑏 | 𝑏B \\$

Which ONE of the languages $𝐿(𝐺)$ is accepted by $G$ ?

A.
$L(G) = \{ a^{2} b^n \mid n \geq 1 \} \cup \{ a^n b^2 \mid n \geq 1 \}$
B.
$L(G) = \{ a^n b^{2n} \mid n \geq 1 \} \cup \{ a^{2n} b^n \mid n \geq 1 \}$
C.
$L(G) = \{ a^n b^n \mid n \geq 1 \}$
D.
$L(G) = \{ a^{2n} b^{2n} \mid n \geq 1 \}$

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Consider the following context-free grammar \(G\), where \(𝑆, 𝐴,\) and \(B\)…