July2016 cs Q24

0. Consider the following two languages : L₁ = {0ⁱ1^j| gcd (i, j) = 1} L₂ is any subset of 0*. Which of the following is correct ?

Answer
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Option : B
Explanation :
L₁ = {0ⁱ1^j| gcd (i, j) = 1}: There are infinite pair having gcd 1. We can't design FA for such language. That's why L₁ is not regular. L₂ is any subset of 0*, we can construct FA for any subset of single alphabet. That's why L₂ is regular. So, option (B) is correct.

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