Tautology

Definition

A tautology is a logical statement that is true in every possible interpretation. It is a formula or assertion that cannot be false regardless of the truth values of its components.

5 Must Know Facts For Your Next Test

1. Tautologies are often used in logical proofs and arguments to establish validity.
2. The standard form of a tautology includes redundant information, making it universally true.
3. In truth tables, a tautology will have all 'true' values in its final column.
4. Tautologies can help simplify complex logical expressions by confirming their validity.
5. Common examples include statements like 'P or not P' (law of excluded middle) and 'If P then P'.

Review Questions

• What makes a statement a tautology?
• How does a truth table for a tautology look?
• Give an example of a simple tautological statement.

Related terms

Contradiction: A statement that is false in every possible interpretation.

Logical Equivalence: Two statements that always have the same truth value in every possible scenario.

Biconditional Statement: A compound statement formed by combining two conditionals, represented as 'P if and only if Q', which is true when both parts have the same truth value.