A discussion in IMT 530 reminded me of tautologies – essentially, logical assertions based on variables. Using tautologies, you can construct what are called truth tables – tables that show when a particular condition holds. Thus, if I treat two variables – A and B as boolean values (true/false), then ask what happens when we apply the AND operation and OR operation to these two variables separately, you end up with a table that looks like this:
|A||B||A AND B||A OR B|
This skips the formal notation. You can go further – there are inference notations, NOT notations (an inversion), and I believe there may also be NOR and NAND (not or and not and), though these operations may simply be a combination of the AND/NOT or OR/NOT formulations rather than formal expressions.