GATE | GATE CS 2020 | Question 18

Consider the following statements.

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 ?
(A) Ⅰ only
(B) Ⅱ only
(C) Both Ⅰ and Ⅱ
(D) Neither Ⅰ nor Ⅱ

Answer: (D)

Explanation: Counter examples for given statements:

I. (anbn) ∪ (a*b*) = a*b*  

where, a*b* is regular but (anbn) is not regular language.

II. Φ ∪ (ab) ∪ (a2b2) ∪ (a3b3) ..... (infinite union) = (anbn)  

where, each language in left side are regular language, but language in right side (anbn) is not regular language.

So, both statements are false.

Option (D) is true.

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