Let M be a DFA given below

Let L(M) be the language generated by the above DFA. Then the complement of L(M) is

{w | n_{a} (w) \geq 3, w ϵ (a, b)^{*}}

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{w | n_{a} (w) = 2, w ϵ (a, b)^{*}}

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{w | n_{a} (w) \leq 3, w ϵ (a, b)^{*}}

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{w | n_{a} (w) \geq 1, w ϵ (a, b)^{*}} \cap {w | n_{a} (w) \leq 3, w ϵ (a, b)^{*}}

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Solution

The correct option is D ${w | n_{a} (w) \geq 1, w ϵ (a, b)^{}} \cap {w | n_{a} (w) \leq 3, w ϵ (a, b)^{}}$
$L (M) = {w | n_{a} (w) = 0 or n_{a} (w) \geq 4}$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯ ¯ L (M) = L (¯ M) = {w | 1 \leq n_{a} (w) \leq 3}$

So, option (d) is correct.

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