Which of the following languages is generated by the given grammer ?

$S \to a S ∣ b S ∣ ϵ$

{a, b}^{*}

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{a^{n} b^{m} ∣ n, m \geq 0}

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{a^{n} ∣ n \geq 0} \cup {b^{n} ∣ n \geq 0} \cup {a^{n} b^{n} ∣ n \geq 0}

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{w ϵ {a, b}^{*} ∣ w h a s e q u a l n u m b e r o f a^{'} s a n d b^{'} s}

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Solution

The correct option is A ${a, b}^{}$
G : $S \to a S ∣ b S ∣ ϵ$

L(G) = ${a, b}^{} .$

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G_{1} : S \to a S b ∣ T, T \to c T ∣ ϵ

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T h e l a n g u a g e L (G_{1}) \cap L (G_{2}) i s

S \to S a S ∣ a S b ∣ b S a ∣ S S ∣ ϵ

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