This is coming from my introduction to topology class.

"Let (Y, d') be a subspace of the metric space (X, d). Prove that a subset is an open subset of (Y, d') iff there is an open subset O of (X, d) such that . Prove that a subset . For a point , prove that a subset is a neighbohood of a iff there is a neighborhood N of a in (X, d) such that "

How and where do I start with this? The definition of a open subset?

A subset O of a metric space is said to be open if O is a neighborhood of each of its points.