Regular Languages UGC

Question 1

Consider the following two languages: L​₁​ = {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 L​₁​ and L₂​ are regular languages
• Both L​₁​ and L₂​ are not regular languages
• Only L​₁​ is regular language
• Only L​₂ is regular language