Truth Table Generator
Enter a Boolean expression using AND, OR, NOT, XOR, and IMPLIES. This tool generates the complete truth table, counts true and false rows, and flags tautologies or contradictions.
Boolean Expression
Operators: AND (&), OR (|), NOT (!), XOR (^), IMPLIES (=>). Variables: A, B, C, D
Truth Table
| A | B | Result |
|---|---|---|
| F | F | F |
| F | T | F |
| T | F | F |
| T | T | T |
Reference Guide
Boolean Operators
AND returns true only when both inputs are true. OR returns true when at least one input is true. NOT flips the value. XOR returns true when exactly one input is true.
Implication
A IMPLIES B is false only when A is true and B is false. In all other cases (including when A is false), the implication is true.
Tautologies and Contradictions
A tautology is an expression that is true for every possible input combination. A contradiction is always false. These are fundamental concepts in propositional logic.
De Morgan's Laws
Two important equivalences for simplifying expressions.