Question: Problem 1 8 . Prove that for any infinite regular language L , there exist two infinite regular languages L 1 , L 2 such

Problem 18. Prove that for any infinite regular language L, there exist two infinite regular languages L1,L2 such that L=L1L2 and L1L2=O?. Here are some hints.
Let D be any DFA and q be any one of its states. Prove that the language
Lq={x|xinL(D) and the run ofDonx visits qan odd number of times }
is regular.
2. Recall the proof of the pumping lemma.
Problem 18. Prove that for any infinite regular language L, there

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