Consider the following language.

L = {x $$ \in $$ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3}

The minimum number of states in a DFA that accepts L is ______.

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?

Consider the language
L = { $${a^n}|n \ge 0$$ } $$ \cup $$ { $${a^n}{b^n}|n \ge 0$$ }
and the following statements.

I. L is deterministic context-free.
II. L is context-free but not deterministic context-free.
III. L is not LL(k) for any k.

Which of the above statements is/are TRUE?