Question

Consider the following statements:

$S_1:\{0^{2n}\mid n\ge 1\}$ is a regular language

$S_2:\{0^m{1}^n{0}^{m+n}\mid m\ge 1andn\ge 1\}$ is a regular language

Which of the following is true about $S_{1}and{S}_2$?

• A. $\text{Both}$ $S_1$ $\text{and}$ $S_2$ $\text{are correct}$
  
• B. $\text{Only}$ $S_1$ $\text{is correct}$
• C. $\text{Only}$ $S_2$ $\text{is correct}$
• D. $\text{None of}$ $S_1$ $\text{and}$ $S_2$ $\text{are correct}$

Answer 1

The correct option is B $\text{Only}$ $S_1$ $\text{is correct}$

$L_1=\{0^{2n}\mid n\ge 1\}$

$L_1$ produces languages having even number of 0's which is regular language.

Regular expression for $S_1$ is $00(00{)}^{\ast }$

$L_2=\{0^m{1}^n{0}^{m+n}\mid m\ge 1andn\ge 1\}$ is context free languages not regular. (m occurs in two places, so there is comparison of count).

So, $S_1$ is correct but $S_2$ is not correct.