Question

Prove that language Lon {a, b}, L={v | V = VR} is not regular.

With Proper Steps and explanation

Answer 1

L = {v | v = v^R } v belongs to {a,b}
L is not regular
proof using pumping lemma:
let take a string w belongs to L
w= aabaa
now divide w into xyz
a|a|baa
x|y|z
x=a,y=a,z=baa
by pumping lemma
for all 0<i xy^iz belongs to L
let i=1, xy^1z = aabaa belongs to L
i=2, xy^2z = xyyz = aaabaa doesn't belongs to L
since for i=2, xy^2z doesn't belongs to L, which violates
pumping lemma, hence L is not regular

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