Truth table generator

Generate a truth table for any logical expression. Supports AND, OR, NOT, XOR, IMPLIES (→), and IFF (↔).

Expression

Operators

Logical operators

AND (∧): True only when both operands are true.

OR (∨): True when at least one operand is true.

NOT (¬): Flips true ↔ false.

XOR (⊕): True when exactly one operand is true (exclusive or).

IMPLIES (→): p → q is false only when p is true and q is false.

IFF (↔): True when both operands have the same truth value.

How truth tables work

A truth table lists every possible combination of truth values for the variables, then evaluates the expression for each combination. With n variables, there are 2ⁿ rows.

Classification

Tautology: Always true (e.g., p or not p).

Contradiction: Always false (e.g., p and not p).

Contingent: Sometimes true, sometimes false.