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From LogicWiki

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	${\displaystyle (A\vee \neg A)}$
T	T
F	T

A	${\displaystyle \neg (A\wedge \neg A)}$
T	T
F	T

Here's a less common tautology:

A	B	${\displaystyle ((B\to A)\wedge (A\vee B))\to A}$
T	T	T
T	F	T
F	T	T
F	F	T