GATE Papers >> CSE >> 2017 >> Question No 116

Question No. 116 CSE | GATE 2017

Identify the language genrated by the following grammar, where S is the start variable

$\begin{array}{l}S\rightarrow XY\\X\rightarrow aX\;\vert a\\Y\rightarrow aYb\;\vert\in\end{array}$


Answer : (C) $\style{font-family:'Times New Roman'}{\{a^mb^n\vert m>n,\;n\geq0\}}$


Solution of Question No 116 of GATE 2017 CSE Paper

         $ \begin{array}{l}S\rightarrow XY\\X\rightarrow aX\vert a\Rightarrow\;\;\;X\rightarrow\left\{a^m\vert m\geq1\right\}\\Y\rightarrow aYb\vert\in\Rightarrow Y\rightarrow\left\{a^nb^n\vert n\geq0\right\}\\S\rightarrow XY\Rightarrow\;\;\;\;\;\;S\rightarrow\left\{a^mb^n\vert m>n,\;n\geq0\right\}\end{array} $

$m > n$ because at least 1 will be attached on left of $ a^nb^n. $

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