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.