Are Regular Languages Closed under Infinite Union?

Here we look at a GATE 2020 exam problem about two statements regarding regular languages, and asking which of them is true (or neither). The first asks if the union of two languages implies both of the original languages are regular, and the second concerns closure under infinite union for regular languages. Watch the video to figure out why the answer is false for both!

▶ADDITIONAL QUESTIONS◀
1. What if instead of union for #1, we had L1 concatenated with L2?
2. Are regular languages always closed under *finite* unions?

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▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.

[siddhantdash]

It would be really helpful if you could select some previous year good questions from GATE exam and solve them.

[waynee]

Before watching the video fully my answers to the questions were false for both too. Although to proof the 1st question I used the the union of L = {a^nb^n | n >= 0} u {a*b*} = {a*b*}.
EDIT: Fixed typo.