Define a regular expression $R$ and explain how this gives rise to a language $\mathcal{L}(R)$.

Define a deterministic finite-state automaton $D$ and the language $\mathcal{L}(D)$ that it accepts.

State the relationship between languages obtained from regular expressions and languages accepted by deterministic finite-state automata.

Let $L$ and $M$ be regular languages. Is $L \cup M$ always regular? What about $L \cap M$ ?

Now suppose that $L_{1}, L_{2}, \ldots$ are regular languages. Is the countable union $\bigcup L_{i}$ always regular? What about the countable intersection $\bigcap L_{i}$ ?