Truth table generator
Build the truth table of any logical expression with AND, OR, NOT, implication and biconditional, and see whether it is a tautology or a contradiction.
How to useTruth table generator
Available in: 
Truth table generator: what it is for
Type an expression with variables such as p, q and r and the logical connectives: negation, conjunction, disjunction, conditional, biconditional and exclusive or. The tool builds every row of the truth table and classifies the proposition.
It accepts several ways of writing the symbols (~, ¬, ^, ∧, v, ∨, ->, →, <->, ↔) and has buttons to insert them. It shows the result as T/F or 1/0.
How to use
- Type the logical expression or use the symbol buttons.
- Check the table with every combination.
- See whether it is a tautology, a contradiction or a contingency.
When to use it
- Studying logic for exams.
- Doing discrete math exercises.
- Checking logical conditions in programming.
Frequently asked questions
Which operators can I use?
Negation (~, ¬, !, not), conjunction (^, ∧, &, and), disjunction (v, ∨, |, or), implication (->, →), biconditional (<->, ↔) and exclusive or (xor, ⊕). Use parentheses to group.
What is a tautology?
An expression that is true in every row of the table. If it is false in every row, it is a contradiction; if it has both results, it is a contingency.
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.