Tautology

A tautology in predicate logic is a statement that is always true, regardless of the truth values of its components. For example, the statement "It is raining, or it is not raining" is a tautology because one of the two options must be true. Tautologies are important in logical reasoning and mathematics because they help establish truths that hold under all circumstances, serving as foundational principles for constructing arguments and proofs. Essentially, if a statement's truth is guaranteed in every possible situation, it is considered a tautology.