Proving Metric Space Containment: A Challenge

[catcherintherye]

Homework Statement

i am required to prove whether the following statement is true or false,

Homework Equations

there exists a metric space (X,d) with B1 contained in B2 contained in
X such that B1=Bo(x1,3), B2=Bo(x2,2), and B2-B1 not equal to the empty set

here Bo denotes the open ball

The Attempt at a Solution

any hints on how to set about this problem?

 

[Dick]

Ok, so your space has to contain at least 3 points, right? x1, x2 and some x in B2-B1. Can you define a metric on those three points that doesn't break any rules (like triangle inequality) and satisfies all of the relations?