A tautology is a logical proposition with a special property: It is true under all circumstances. This property can be defined more precisely. Logical propositions are made up of basic propositions (usually symbolized by lower-case letters, sometimes italicized; p, q, etc.) joined together by connectives. Typically these connectives include "not" (negation), "and" (conjunction) "or" (disjunction), and the "if-then" relation (implication). Each basic proposition can be assigned a truth-value - either true (T) or false (F). Then the truth of a compound sentence built out of basic propositions and connectives can be calculated with the help of truth functions or truth tables.

A logical proposition is a tautology if it is true regardless of the truth-values of its basic propositions. The final column in a tautology's truth table would consist entirely of T's.

Consider an example: " p or not-p" (e.g. "Elvis is alive or Elvis is not...