Q42

MSQ2 marks

Let $\Sigma=\{a, b, c\}$ . For $x \in \Sigma^{*}$ , and $\alpha \in \Sigma$ , let $\#_{\alpha}(x)$ denote the number of occurrences of $\alpha$ in $x$ . Which one or more of the following option(s) define(s) regular language(s)?

(A)

$\left\{a^{m} b^{n} \mid m, n \geq 0\right\}$

(B)

$\{a, b\}^{*} \cap\left\{a^{m} b^{n} c^{m-n} \mid m \geq n \geq 0\right\}$

(C)

$\left\{w \mid w \in\{a, b\}^{*}, \#_{a}(w) \equiv 2(\bmod 7)\right.$ , and $\left.\#_{b}(w) \equiv 3(\bmod 9)\right\}$

(D)

$\left\{w \mid w \in\{a, b\}^{*}, \#_{a}(w) \equiv 2(\bmod 7)\right.$ , and $\left.\#_{a}(w)=\#_{b}(w)\right\}$

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