It's a bit strange that nobody mentioned Boolean algebra: https://en.wikipedia.org/wiki/Boolean_algebra

Could you perhaps be a little more specific? Sure, we use OR, AND, and even XOR to deal with conditionals that map to T and F, but this seems like kind of a surface level use of booleans. When do we invoke the algebraic properties of the structure when coding?

De Morgan's laws! I am sure people use it routinely to simplify complicated boolean expressions while writing code or mentally simplify complicated boolean expressions while reading code.

And then you can probably reduce it with a Karnaugh map. It's pretty neat.

You probably didn't know Byook:

http://www.byook.com/