Enter Logic Argument
Example Data Table
| Argument Type | Premises | Conclusion | Expected Result |
|---|---|---|---|
| Modus Ponens | P -> Q P |
Q | Valid |
| Affirming the Consequent | P -> Q Q |
P | Invalid |
| Disjunctive Syllogism | P | Q ~P |
Q | Valid |
| Hypothetical Syllogism | P -> Q Q -> R |
P -> R | Valid |
Formula Used
An argument is valid when no truth assignment makes all premises true and the conclusion false.
Core test:
(P1 ∧ P2 ∧ ... ∧ Pn) → C
Valid condition: the core test is true on every row.
Invalid condition: at least one counterexample row exists where all premises are true and the conclusion is false.
How to Use This Calculator
- Enter each premise on a separate line.
- Enter the conclusion in the conclusion box.
- Use symbols such as
~,&,|,->, and<->. - Add a variable order when you want a custom truth table layout.
- Press calculate to show the result above the form.
- Use the CSV or PDF buttons to save the visible output.
Validity Logic Calculator Guide
Why Validity Matters
Validity is a structural property of an argument. It does not ask whether the real world supports each sentence. It asks whether the conclusion must follow when the premises are assumed true. This difference is important. A valid argument can contain false premises. An invalid argument can contain a true conclusion. The calculator focuses on form, not factual content.
How the Truth Table Works
The tool first detects every symbol used in the premises and conclusion. It then builds every possible true or false assignment. Each row becomes a small test case. The premises are evaluated under that assignment. The conclusion is evaluated under the same assignment. If all premises are true and the conclusion is false, the row is a counterexample. One counterexample is enough to make the argument invalid.
Useful Study Features
This calculator supports common connectives used in introductory and advanced logic classes. You can type negation, conjunction, disjunction, conditional, biconditional, and exclusive or. Parentheses help control order. The variable order field is useful when your course expects tables in a specific arrangement. The summary area also reports whether the premises are consistent and whether the conclusion is a tautology, contradiction, or contingent statement.
Reading the Result
A valid result means the truth table found no failing row. It does not prove the premises are actually true. It proves the inference pattern preserves truth. An invalid result means the table found a possible case where the premises hold but the conclusion does not. Review highlighted rows carefully. They show exactly why the inference fails.
Common Mistakes
A frequent mistake is testing only rows where the conclusion is true. Validity requires checking rows where premises are true. Another mistake is reading conditional statements as causal claims. In formal logic, a conditional only fails when the left side is true and the right side is false. Always use parentheses when mixing several operators with care.
Exporting Your Work
Use the CSV download for spreadsheet review. Use the PDF download for notes, homework checks, or discussion. Keep the displayed row limit high when you want the export to include more of the table.
FAQs
1. What does logical validity mean?
Logical validity means the conclusion cannot be false when all premises are true. It depends on the argument structure, not on whether the statements describe real facts.
2. Which operators can I enter?
You can use negation, and, or, exclusive or, implication, and biconditional operators. Common forms include ~, !, &, |, xor, ->, and <->.
3. What is a counterexample row?
A counterexample row makes every premise true and the conclusion false. Its existence proves the argument form is invalid.
4. Does a valid argument always have true premises?
No. Validity only tests whether the conclusion follows from the premises. Soundness requires both validity and actually true premises.
5. Why are parentheses useful?
Parentheses remove ambiguity. They force the calculator to evaluate grouped parts before applying other operators.
6. How many variables can I use?
The calculator supports up to ten unique variables. More variables create very large truth tables and reduce readability.
7. What does inconsistent premises mean?
It means no truth table row makes every premise true at once. Such arguments are valid in the technical truth-table sense.
8. Can I export the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a formatted report of the visible result and table.