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Applied Course | Mock GATE | Test 1 | Question: 14

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Consider the following regular expression over the alphabet $\Sigma = \{0, 1\}$
$$\text{RE} =\Sigma ^* 1 \Sigma^* $$
The complement of the language generated by given $\text{RE}$ is

  1. $L= \{ w \mid w \text{ contains substring 1 }$
  2. $L=\{ w \mid w \text{ contains at least 1 }$
  3. $L=\{ w \mid w \text{ does not contain substring 1 }$
  4. $L=\{ w \mid w \text{ contains exactly 1}$
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Given $\Sigma=\{0, 1\} \: \: \: \text{substitute } \Sigma = \{0, 1\}$
$\text{RE}$ is $(0+1)* 1(0+1)*$
$\text{DFA}$ that accepts $1$ generated by $\text{RE}$ is
Applied Course 2019 Mock1-14
Accepts all strings of $0$'s including $\epsilon$
$\{ \epsilon, 0, 00, 000, \dots \}$
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