Hi Janet,
The 9 volt you mention makes me think this is a
unit run from a battery.
You say if one wire recieves a signal,
the other two should become open circuit,
i hope i have that right.
So its a kind of race?
Whichever goes first,
would cut off the other two ?
You say you were thinking of a relay,
but you reckoned six relays for that?
No, i think one for each wire would do.
I have drawn out a set of three relays,
i hope it meets your needs.
Any wire operating, will cut off the other two.
Ive drawn the contacts above the coils for each,
i think it makes it easier to follow like that.
If its a battery unit, maybe you should consider
using chips instead, because of the current
needed for relay coils.
Best of luck with it,
John