# Using Mathematical Logic To Wire a 3-way Switch - By Michael
Sakowski
A 3-way switch allows one to turn a light on or off at two
different locations. A friend asked me to explain how these switches
worked. I had never actually installed a 3-way switch network before
but I understood the logic used. The 3-way switch network is the
logical equivalent of an "if-and-only-if" statement. In a P
if-and-only-if Q statement, the statement is true if both parts P and
Q are true or both parts P and Q are false. In an analogous
manner, the circuit running through a pair of 3-way switches is only
completed if both switches are in the "up" position or if both
switches are in the "down" position. The diagram below illustrates
this:
So my conclusion was that one should connect the two switching
terminals from the first switch to the two switching terminals of the
second switch. This leaves a 3rd terminal on each switch to connect to
the power supply (1st switch) and the load (2nd switch). My
explanation proved to be correct.
This episode clearly illustrated that the logic used in proofs of
mathematical theorems had a direct application to a real-life
situation.
Note: Electrical work is dangerous. This
article just describes the logic of a 3-way switch, and is not
intended, in any way, as wiring instructions. Hire a qualified
electrician to make electrical repairs. |