Tautology

Tautology

Introduction to Logic and Probability

Published in Sriraman Sridharan, R. Balakrishnan, Foundations of Discrete Mathematics with Algorithms and Programming, 2019

Sriraman Sridharan, R. Balakrishnan

A compound proposition is called a tautology if its truth value is always true irrespective of the truth values of its constituents. For example, p∨¬p $ p\vee \lnot p $ is always true, hence it is a tautology. If the propositional expression always takes the truth value false, then it is called a contradiction. For example, p∧¬p $ p \wedge \lnot p $ is a contradiction.

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Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018

Dan Zwillinger

A statement such as (p → (q ∧ r)) ∨ ¬p is a compound statement composed of the atomic propositions p, q, and r. The letters P, Q, and R are used to designate compound statements. A tautology is a compound statement which always is true, regardless of the truth values of the atomic statements used to define it. For example, a simple tautology is (¬¬p) ↔ p. Tautologies are logical truths. More examples:

Algebraic semantics for propositional superposition logic

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Published in Journal of Applied Non-Classical Logics, 2020

Athanassios Tzouvaras

is a -tautology. However () is not a -tautology for any .

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Introduction to Logic and Probability

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Algebraic semantics for propositional superposition logic