MandysNotes

Sunday, 06 April 2014 00:00

Tautology

By  Gideon
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Imagine your friend tells you that the animal he is thinking of is either duck-billed or not duck-billed.

In other words, he is telling you that either \(A\) is true, or \( \lnot A\) is true.

Equivalently he is telling you that the statement:

\[ A \cup \lnot A\]

is true. 

This is not very helpful in geussing which animal he is thinking of, but it does have the property of always being true.

In other words, the statement 

\[ A \cup \lnot A\]

is true if \(A\) is true (and hence \(\lnot A\) is false);

it is also true if \(A\) is false (and hence \(\lnot A \) is true).

Such a statement is called a tautology.

A tautology must have a truth table with all "T"s under it.

The truth table for \(A \cup \lnot A\) is as follows:

TautologyTT1

Read 2716 times Last modified on Tuesday, 30 December 2014 01:49
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