Tautologies

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
T T T T
T F F T
F T F T
F F T F

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.