Proving Metric Equivalence for Subset Y in Metric Space X

[selzer9]

Y ⊂ X where X is a metric space with the function d. Prove that (Y,d) is a metric space with the same function d.

The metric function d: X x X -> R.

I know that the function for Y is:

d* : Y x Y -> R

How do I show that d is the same as d*.

 

[jbunniii]

What is the definition of a metric?