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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...

This section contains 407 words(approx. 2 pages at 300 words per page) |