1. The problem statement, all variables and given/known data Does A [itex]\subset[/itex]B imply d(B,C)<=d(A,C)? 3. The attempt at a solution So my feeling is yes. But trying to prove this is difficult. se we know A [itex]\subset[/itex]B Suppose C intersection B isn't empty then d(B,C)=0<=d(A,C) is true since distance is always non-negative. Suppose C intersection B is empty. How to prove it in this case I can't do. Any pointers?