Gate2020 cs Q32

32Consider the following sentences.
I. If L₁ ⋃ L₂ is regular, then both L₁ and L₂ must be regular.
II. The class of regular languages is closed under infinite union.
Which of the above statements is/are TRUE?

Option : B
Explanation :
Let L₁ = an bn⇒ CFL
L₂ = Σ* ⇒ Regular
L₁ ∪ L₂ = (aⁿ bⁿ) ∪ Σ* = Σ* ⇒ Regular
Since L₁ ∪ L₂ is regular but L₁ is not regular, Hence statement I is false.
Regular language is not closed under infinite union.
Hence, statement-II is also false.
∴ Neither I nor II is true.

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