Which one of the following regular expressions represents the set of all binary strings with an odd number of 1’s?

Consider the following statements.

I. If L₁ $$ \cup $$ 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?

If L is a regular language over Σ = {a, b}, which one of the following languages is NOT regular?

For Σ = {a, b}, let us consider the regular language L = {x | x = a^2+3k or x = b^10+12k, k ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?