Tautologies

In propositional logic, a tautology is a statement that is always true, regardless of the truth values of its individual components. Think of it as a conclusion that must always hold, no matter what specific facts you plug into it. For example, the statement "It is either raining or it is not raining" is a tautology because one of those two options will always be true. Tautologies are important in logic and mathematics because they help us understand structures of reasoning and ensure that arguments are valid, standing firm regardless of the circumstances.