Metric spaces, open sets, and closed sets

I have these two propositions stated in my book as follows.

Proposition 1.

Let $\displaystyle (X,d) $ be a metric space, then

a) The sets $\displaystyle X$ and $\displaystyle \emptyset$ are open

b) Any finite intersection of open sets is open

c) Any union of open sets is open.

Similarly,

Proposition 2.

Let $\displaystyle (X,d)$ be a metric space, then

a) The sets $\displaystyle X$ and $\displaystyle \emptyset$ are closed.

b) Any finite union of closed sets is closed

c) Any intersection of closed sets is closed.

I understand parts b) and c) of both propositions. However, I have no clue why a) is listed for both and why a) is important. What is a) telling us? If someone could please explain to me the meaning of a) in both cases it would be much appreciate. Thank you very much.