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A truth table is a mathematical table used in logic, specifically in Boolean algebra and propositional calculus, to determine the truth value of a compound statement based on the truth values of its individual components. It lists all possible combinations of truth values for the propositional variables involved in a statement and then shows the resulting truth value for the entire statement for each combination.

The construction of a truth table begins with identifying the atomic propositions, which are the simplest statements that can be either true or false. For a statement with 'n' atomic propositions, there will be 2^n possible combinations of truth values. Each row in the table represents one such combination. The columns of the table typically include the atomic propositions, intermediate compound statements, and finally, the main compound statement. Logical operators such as AND (conjunction), OR (disjunction), NOT (negation), IMPLIES (conditional), and IF AND ONLY IF (biconditional) are used to connect these propositions.

Truth tables are instrumental in verifying logical equivalences, determining the validity of arguments, and understanding the behavior of logical circuits. For example, a truth table can prove that (P AND Q) OR R is not logically equivalent to P AND (Q OR R) by showing that there is at least one row where their truth values differ. They are a fundamental tool in computer science, philosophy, and mathematics for analyzing and constructing logical arguments.