1.9k views

Which of the following are regular sets?

1. $\left\{a^nb^{2m} \mid n \geq 0, m \geq 0 \right\}$

2. $\left\{a^nb^m \mid n =2m \right\}$

3. $\left\{a^nb^m \mid n \neq m \right\}$

4. $\left\{xcy \mid x, y, \in \left\{a, b\right\} ^* \right\}$

1. I and IV only
2. I and III only
3. I only
4. IV only
edited | 1.9k views

Since in option 2 and 3, $n$ is dependent on $m$, therefore a comparison has to be done to evaluate those and hence are not regular.

I and IV are clearly regular sets.

edited by
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if option D were
xcx then both x,c should belong to (a+b)* , right ?
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how option d is regular here ? for this c should belong to (a + b)^(*) it is not as it will give only c on keeping x as epsilion
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@Leensharma can you explain option d)
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d) *IS* regular. The regular language for d) will be (a+b)*c(a+b)*
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can you explain how 1st is regular by some explanation?
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@Shubham Aggarwal I Think first can be written as -->(a)*(bb)* . Here both asterisks are independent of each other and can be thought as n and m.

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