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

Consider the following two languages :

L_{1} = {0^{i}1^{j}| gcd (i, j) = 1}

L_{2} is any subset of 0*.

Which of the following is correct ?**(A)** L_{1} is regular and L_{2}* is not regular**(B)** L_{1} is not regular and L_{2}* is regular**(C)** Both L_{1} and L_{2}* are regular languages**(D)** Both L_{1} and L_{2}* are not regular languages**Answer:** **(B)****Explanation:** L_{1} = {0^{i}1^{j}| gcd (i, j) = 1}:

There are infinite pair having gcd 1. We can’t design FA for such language. That’s why L_{1} is not regular.

L_{2} is any subset of 0*, we can construct FA for any subset of single alphabet. That’s why L_{2} is regular.

So, option (B) is correct.

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