UGC-NET | UGC NET CS 2016 July – III | Question 24

Consider the following two languages :
L₁ = {0ⁱ1^j| gcd (i, j) = 1}
L₂ is any subset of 0*.
Which of the following is correct ?
(A) L₁ is regular and L₂* is not regular
(B) L₁ is not regular and L₂* is regular
(C) Both L₁ and L₂* are regular languages
(D) Both L₁ and L₂* are not regular languages

Answer: (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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