Identify the language generated by the following grammar, where S is the start variable.
$S \to X Y$
$X \to a X | a$
$Y \to a Y b | ϵ$

{a^{m} b^{n} | m > n, n > 0}

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{a^{m} b^{n} | m \geq n, n > 0}

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{a^{m} b^{n} | m \geq n, n \geq 0}

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{a^{m} b^{n} | m > n, n \geq 0}

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Solution

The correct option is D ${a^{m} b^{n} | m > n, n \geq 0}$
$S \to X Y$
$X \to a X | a \Rightarrow X \to {a^{m} | m \geq 1}$
$Y \to a Y b | ϵ \Rightarrow Y \to {a^{n} b^{n} | n \geq 0}$
$S \to X Y \Rightarrow S \to {a^{m} b^{n} | m > n, n \geq 0}$
m > n because at least 1 will be attached on left of $a^{n} b^{n}$ .

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