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GATE | GATE CS 2020 | Question 18

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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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Last Updated : 01 Oct, 2021
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