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# Tautology

A Tautology is a sentence that is always true, independent of the way the world is. There are many different ways to describe what it means to be a tautology: true independent of the facts, true in virtue of logical form, true in virtue of meaning, and so on.

## Truth Table Test for Tautology

To determine whether a sentence is a tautology, construct a truth table for it. After you fill out the truth table, look under the main connective of the sentence. If all you see is T, then you've got a tautology!

## Examples

Here are two common tautologies:

A $\left(A\vee ¬A\right)$
T T
F T
A $¬\left(A\wedge ¬A\right)$
T T
F T

Here's a less common tautology:

A B $\left(\left(B\to A\right)\wedge \left(A\vee B\right)\right)\to A$
T T T
T F T
F T T
F F T