Consider the following two languages: L1 = {x | for some y with | y| = 2|x| , xy ∈ L and L is regular language} L2 = { x | for some y such that |x| = |y| , xy ∈ L and L is regular language} Which one of the following is correct?

Both L1 and L2 are regular languages

Both L1 and L2 are not regular languages

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Regular Languages UGC

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Question 1

Consider the following two languages: L₁ = {x | for some y with | y| = 2^|x| , xy ∈ L and L is regular language} L₂ = { x | for some y such that |x| = |y| , xy ∈ L and L is regular language} Which one of the following is correct?

Both L₁ and L₂ are regular languages
Both L₁ and L₂ are not regular languages
Only L₁ is regular language
Only L₂ is regular language

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