Just like to correct an apparent misunderstanding here. TCAS equipped aircraft will receive RA's when in conflict with non TCAS traffic so long as that aircraft has a functioning mode "C" transponder. If mode "C" is not present then an TA will be given.
The full TCAS operating environment has the added advantage of RA's being co-ordinated where both aircraft are equipped but the system still funtions if only one aircraft is. That is why ATC sometimes get low level VFR traffic to stop mode "C" if they pass under a busy approach or get the TCAS aircraft to select TA only..........