# CSC 226 Chapter Notes - Chapter 1.4: Logical Equivalence

## Document Summary

Tautology: a compound proposition that is always true, regardless of the truth values of the individual propositions within it: example: p(cid:1166) p p. Contradiction: a compound proposition that is always false, regardless of the truth values of the individual propositions within it: example: p (cid:1165) p p. You can prove tautologies and contradictions using truth tables. True or all false then it is a tautology or contradiction, respectively; but if there is at least one instance of having both true and false final values it cannot be either. Logically equivalent: when two compound propositions have the same truth value regardless of their individual propositions. De morgan"s laws: logical equivalences that show how to correctly distribute a negation operation inside a parenthesized expression. There are two of them, though they are just reversed version of each other. For their explanations, use these propositions: p: the patient has migraines, q: the patient has high blood pressure.