Totuustaulu

Totuustaulu, or truth table, is a tool used in propositional logic to display the truth value of a compound proposition for every possible combination of truth values of its basic components. It helps to analyze how logical connectives and expressions behave under all scenarios.

A truth table lists all possible assignments of truth values to the involved variables. If there are n variables, the table has 2^n rows. Each row shows a specific combination of true and false values, and a column (or columns) shows the resulting truth value of the expression under that combination. In practice, tables may also include intermediate columns for subexpressions to make the evaluation clear.

Truth tables are used to determine logical properties such as equivalence, validity, tautology, and satisfiability. They provide a straightforward way to test whether two statements have the same truth value in every possible case. Beyond pure logic, truth tables are foundational in the design and verification of digital circuits, where logical connectives correspond to logic gates and the table describes circuit behavior.

Example: the truth table for the conjunction p ∧ q

p q | p ∧ q

true true | true

true false | false

false true | false

false false | false

This compact representation makes it easy to reason about complex expressions and to compare different formulations.