Regular languages

Question

If $L1$ is regular and $L2$ is a subset of $L1$, then which of the following has to be regular ?

(a) $L2$     

(b) $L1\cap L2$   

( c) $L2^{n}$  

⁽ d) $L1^{n}$

Answer 1

Let L1=(a+b)^*  and L2=a^mb^m 

Here L2 is subset of L1 but it is not regular. 

L1 intersection L2 will give L2 ONLY which is non regular.

((a+b)*)ⁿ  is also regular.

But (a^mb^m)^{n is not regular since we need to count here number of a's equal to number of b's.}

Comments

how is ((a+b)*)ⁿ regular?

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draw dfa for (a+b)^*  and run it more n times will it change anything ?? i dont think so

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okay okay i got it. Thanks!