Boolean logic truth tables
Build complete truth tables, classify formulas and compare logical equivalence with counterexamples.
One to eight formulas, one per line, using at most 12,000 characters. Use up to 12 case-sensitive ASCII variables, 512 tokens per formula and 64 nested operations. All assignments are enumerated, with one row for a constant formula. Supported operators: NOT, AND, XOR, OR, implication and equivalence, in that precedence order. Implication associates to the right. No input code is executed. One formula per line. Use parentheses, Boolean operators and case-sensitive variables. Results update as you type. Up to 12,000 characters.
Your result
How to use Boolean logic truth tables
- Enter a formula on each line. Use parentheses to make the intended grouping clear.
- Read the complete truth table. T means true and F means false.
- Read classifications and equivalence checks in the report. For a non-equivalent pair, inspect its counterexample.
Useful next steps
What the result shows
A tautology is true for every assignment. A contradiction is false for every assignment. Other formulas are contingent. Equivalent formulas agree on every assignment to their combined variables.
Operator order
NOT binds before AND, then XOR, OR, implication and equivalence. Use parentheses when in doubt. Variables such as A and a are different; true, false, 1 and 0 are constants.
Keep the full result
CSV contains every assignment; JSON includes classifications and exact counterexamples. The text report explains the formula labels. Processing stays on your device.