Tautology, Contradiction, and Contingency | Tautology in Logic

Tautology in Logic: Tautology, contradiction, and contingency classify propositional statements by their truth values: a tautology is always true, a contradiction is always false, and a contingency can be either true or false depending on variable assignments. These concepts are determined using truth tables, examining if the final column shows all True (tautology), all False (contradiction), or a mix (contingency).

Lets see the following example. For a proposition P, consider the statement “P and not P”. This statement is always false whatever truth values P takes. So it’s a Contradiction.

Tautology

A statement which is true for all possible values of its propositional variables is called tautology.

For example, lets consider the statement “p or not p” where p is a proposition. This is a tautology, because it is always true regardless the truth values of p.

This is why, “It is raining or it is not raining” (p∨~p) is an example of a tautology.

Contradiction

A statement which is false for all possible truth values is called a contradiction.

For example, consider the statement “p and not p” where p is a proposition. This is always false whether p is true or false. So it is a contradiction.

“It is raining and it is not raining” (p∧~p) is an example of a contradiction.

Contingency

A statement which is neither true nor false for all possible truth values is called contingency.

For example, “It is raining and the sun is shining” (p∧q) is a contingency.

Truth Table of Tautology, Contradiction and Contingency

Lets understand the truth table of tautology, contradiction and contingency. The same has been described below.

Example of Tautology:

Example of Contradiction:

Example of Contingency:

Related Articles: Mathematical Logic: Logical Connectives, Truth Table