metric spaces

catcherintherye

1. The problem statement, all variables and given/known data

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

2. Relevant 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

3. 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?