Consider the following context-free grammars: \(G_1 : S \to aS \mid B, B \to b…
GATE · 2016 · CS · Set 1 · Computer Science & IT
Consider the following context-free grammars:
\(G_1 : S \to aS \mid B, B \to b \mid bB\)
\(G_2 : S \to aA \mid bB, A \to aA \mid B \mid \varepsilon,B \to bB \mid \varepsilon\)
Which one of the following pairs of languages is generated by \(G_1\) and \(G_2\), respectively?
- A.
\(\{ a^mb^n \mid m > 0 \text{ or } n >0\}\)and\(\{ a^mb^n \mid m > 0 \text{ and } n >0\}\) - B.
\(\{ a^mb^n \mid m > 0 \text{ and } n >0\}\)and\(\{ a^mb^n \mid m > 0 \text{ or } n\geq0\}\) - C.
\(\{ a^mb^n \mid m \geq 0 \text{ or } n >0\}\)and\(\{ a^mb^n \mid m > 0\text{ and } n>0\}\) - D.
\(\{ a^mb^n \mid m \geq 0 \text{ and } n >0\}\)and\(\{ a^mb^n \mid m > 0 \text{ or } n>0\}\)
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Correct answer: D
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