I am taking the GRE in less than 10 days, and I have never taken analysis. And I would like to tackle metric problems and I was wondering if anyone could show me a certain strategy to solve problems as the following.
For every set $S$ and every metric $d$ on $S$, which of the following is a metric on $S$ ?
(A)$4 + d$
I studied on my own and this is what I know about metrics.
If $\delta$ is a metric on $S$ and $x,y,z \in S$
a), $\delta (x,y) \ge 0 ,\forall x,y \in S$
b), $\delta (x,y) + \delta (y,z) \ge \delta (x,z) , \forall x,y,z \in S$
c), $\delta (x,x) = 0 ,\forall x \in S$
I think that (A) is not an answer because $4+d (x,x) = 4 \neq 0$.
For the rest, I have no idea how to proceed...