Choose the regular langauge

Question

L1:{ww^R∣w,x∈{a,b}∗ and |w|>0},w^R is the reverse of string w

L2:{wxw^R∣w,x∈{a,b}∗ and |w|,|x|>0},w^R is the reverse of string w

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1. L1 is regular but not L2
2. L2 is regular but not L1
3. Both L1 and L2 are regular
4. Neither L1 nor L2 is regular

Answer 1

Option B) L1 is not regular, because the string has to be saved to check if it's followed by its reversal. And there's no way to identify the end of the string. So this language is not even a DCFL and is a CFL

L2 is regular because both x and w belong to (a+b)*. Hence any part of the string can be taken a w,X,w^r this grammer generates the set of all strings that atleast start and end with the same charachter.