Truth table

A truth table lists a proposition’s or logical circuit’s output for every possible combination of its inputs. It makes logical behavior explicit and supports testing equivalence and validity.

Logical connective: An operator that combines or modifies propositions to form new propositions. Each connective supplies the rule used to compute a column of the table.
Tautology: A proposition that is true under every possible assignment of truth values to its variables. A final column of all true entries identifies a tautology.
Proposition: A declarative statement that is either true or false. Each input column represents one proposition whose value varies by row.
Venn diagram: A diagram using overlapping regions to represent sets and their relationships. It depicts set relationships spatially, while a truth table enumerates assignments.
Negation: A unary logical operation that reverses a proposition’s truth value. Its output column flips the input value in every row.
Contradiction: A proposition that is false under every possible assignment of truth values to its variables. A final column of all false entries identifies a contradiction.
Truth value: The status assigned to a proposition, conventionally true or false in classical logic. The entries record these values for inputs and compound outputs.
Karnaugh map: A diagram that arranges Boolean function values to reveal simplifications of the function. It reorganizes table outputs so adjacent cases expose reducible logic.
Conjunction: A logical operation that is true only when all its component propositions are true. Its column contains true only on rows where both inputs are true.
Logical equivalence: A relation between propositions that have the same truth value under every assignment of their variables. Matching output columns establish equivalence directly.

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