Let's suppose I wanted to create the states a light switch could be in and the ways I could operate one using a set. The switch looks like this (which is an istock photo from user crrussel):

[![enter image description here](https://i.stack.imgur.com/dqUc4.png)](https://i.stack.imgur.com/dqUc4.png)

Consider a set $L$ of the following elements:

{up, down}

What operation would I use to go from switching up or down? Could it be something like this?

$up + down = down$?

Or would I have to define some operator $switch$ such that it turns element $a \mapsto b$ where $b$ is the other element of the set $L$? Like this:

$switch\ up \mapsto down$

Just trying my hand at understanding a general intuition of sets by creating my own and seeing if my rules hold properly.