Is a mode C transponder required underneath Class C airspace? FAR 91.215 states that a mode C transponder is required for...


  all aircraft in all airspace above the ceiling and within the lateral
  boundaries of a Class B or Class C airspace area designated for an
  airport upward to 10,000 feet MSL


My flight instructor and I disagree on how this regulation is interpreted. He says that I need a transponder to fly underneath class C. I understand it to mean that I only need and transponder if I am both above and within the lateral boundaries (i.e. overflying the airspace). 

Which is the correct interpretation?
You are correct. You do not need a transponder to operate under Class C airspace if there are no other overlapping airspace areas where a transponder is required. In fact, if you read a little further in that reg, you'll see that is one of the places where aircraft built with no electrical system are allowed to fly at all!