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
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.