Given two languages : L1 = {(ab)ⁿ aᵏ | n > k, k ≥ 0}
Given two languages :
L1 = {(ab)ⁿ aᵏ | n > k, k ≥ 0}
L2 = {aⁿ bᵐ | n ≠ m}
Using pumping lemma for regular language, it can be shown that
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Correct answer: (D) L₁ is not regular and L₂ is not regular
Explanation
The pumping lemma for regular languages can only be used to prove that a language is not regular. Both L₁ (which needs to compare n and k) and L₂ (which needs to compare n and m) require unbounded counting, so neither is regular.