Fall 2000, CSE 468: Lecture 3 (Aug 30)

Preliminary notions

Correspondence between equivalence relations and partitions

Classical Logic.

Propositional calculus


Formulas are expressions built on


The letters range on the set of boolean values B = {True, False} The connectives are functions on B. For instance: "p implies q" is the function (of p and q) which returns False when p is True and q is False, and True in all other cases.

Truth tables: a way to represent the meaning of each connective. The meaning (truth value) of more complex formulas can be derived by composing the truth tables.

Tautology: A formula which is True for all the possible truth values of the letters contained in it.


There are variuos systems to derive tautologies (i.e. to prove that a certain formula is a tautology), but usually the simplest method is to use the truth tables.