Size of a maximum matching <= Size of a minimum cover.

Question

So I read that the size of a maximum matching <= the size of a minimum cover. Could someone explain? Thanks!

Answer 1

Let $M$ be any matching and $U$ any vertex cover.

For each edge $uv \in M$, at least one of $u,v$ is in $U$ or else the edge $uv$ is not covered by $U$. Therefore, $|M| \leq |U|$.

It is easier to think of the size of any matching as a lower bound to any vertex cover :)