1. The 3-Way Light Switch and The If-And-Only-If Statement
In a 3-way light switch, the light goes on if both switches are in the up position or if both switches are in the down position. If one switch is up and one is down, the light is off.
In a P If-and-only-if Q statement, the entire statement is true if both parts P & Q are true. The entire statement is also true if both parts P & Q are false. The entire statement is false if one part is true while the other part is false.
Thus, the 3-way switch is analogous to the if-and-only-if statement.
Is this mathematical knowledge helpful to one actually wiring a 3-way switch?

2. ANSWER: Yes, it is helpful to know the math!
The diagram below shows the clear analogy.
For More Info, See How I Used Math To Wire a Switch!