Solver Results
Results appear here above the form after calculation.
Interpretation
Outcome Graph
Truth Table
Calculator Inputs
Use symbols or words. Supported forms include AND, OR, NOT, XOR, IMPLIES, and IFF.
Formula Used
Logical reasoning here is solved with truth-functional evaluation. Every row assigns truth values to variables, then evaluates each statement using standard propositional rules.
Core Operators
- ¬P is true when P is false.
- P ∧ Q is true when both are true.
- P ∨ Q is true when at least one is true.
- P ⊕ Q is true when exactly one is true.
- P → Q is false only when P is true and Q is false.
- P ↔ Q is true when both sides match.
Argument Validity
An argument is valid when there is no row where all premises are true and the conclusion is false.
Validity test: ((P1 ∧ P2 ∧ ... ∧ Pn) → C) must be a tautology.
Consistency test: at least one row must make all premises true together.
How to Use This Calculator
- Enter a main expression if you want a classification result.
- Add premises one per line for argument testing.
- Enter a conclusion to check validity and counterexamples.
- Leave variables blank for automatic detection, or define their order manually.
- Choose row view, order, truth labels, and display limit.
- Click Solve Logical Reasoning to generate summaries, graphs, and the truth table.
- Use the CSV and PDF buttons to export the computed output.
Example Data Table
| Scenario | Premises | Conclusion | Expected Outcome | Why |
|---|---|---|---|---|
| Modus Ponens | A → B; A | B | Valid | Whenever both premises hold, the conclusion must hold. |
| Hypothetical Syllogism | A → B; B → C | A → C | Valid | The chain of implications preserves truth logically. |
| Affirming the Consequent | A → B; B | A | Invalid | B can be true for reasons unrelated to A. |
| Consistency Check | A; ¬A | B | Inconsistent | No row can satisfy both premises together. |
FAQs
1. What does this logical reasoning solver do?
It evaluates logical statements, generates truth tables, tests premise consistency, checks argument validity, identifies counterexamples, and summarizes outcomes with charts and downloadable reports.
2. Which operators can I use?
You can use NOT, AND, OR, XOR, IMPLIES, and IFF. Symbolic versions like ¬, ∧, ∨, ⊕, →, and ↔ are also accepted.
3. What is a counterexample row?
A counterexample row is one where every premise is true while the conclusion is false. Any such row makes the argument invalid.
4. How is validity determined here?
The solver checks all possible truth assignments. If no assignment makes the premises true and the conclusion false, the argument is reported as valid.
5. Why does the tool limit variables?
Truth tables grow exponentially. Eight variables already create 256 rows, which keeps the page responsive while still covering many practical classroom and exam problems.
6. Can I use it without entering premises?
Yes. You can enter only a main expression to classify it as a tautology, contradiction, or contingency and still get a graph plus table.
7. What does consistency mean for premises?
Premises are consistent when at least one truth assignment makes all of them true together. If none exists, the premises are inconsistent.
8. What do the exports include?
The CSV export includes the visible truth table. The PDF export includes summary results and the visible truth table for quick sharing or printing.