Deductive Reasoning Calculator

Analyze arguments, syllogisms, and logical consistency fast. Compare premises, test conclusions, and review outcomes easily. Use guided inputs, exports, examples, and charts for insight.

Calculator

Supported operators: AND, OR, NOT, XOR, ->, =>, <->, IFF, TRUE, FALSE. Use single-letter variables like P, Q, R.

Argument name

Premise 1

Premise 2

Premise 3

Conclusion

Analysis notes

Show only rows where all premises are true

Example Data Table

Argument	Premise 1	Premise 2	Conclusion	Expected result
Modus Ponens	(P -> Q)	P	Q	Valid
Affirming the Consequent	(P -> Q)	Q	P	Invalid
Disjunctive Syllogism	(P OR Q)	NOT P	Q	Valid
Hypothetical Syllogism	(P -> Q)	(Q -> R)	(P -> R)	Valid

Formula Used

Argument is valid if, for every assignment v: [Premise1(v) ∧ Premise2(v) ∧ ... ∧ PremiseN(v)] → Conclusion(v) is true.

Counterexample count = number of assignments where all premises are true and the conclusion is false.

Classification = Valid when counterexamples = 0; otherwise Invalid. If premises never hold together, the result is Vacuously valid.

This calculator uses a truth-table method. It lists every possible truth assignment for the variables, evaluates each premise and the conclusion, then checks whether any counterexample exists.

How to Use This Calculator

Enter up to three premises using single-letter variables.
Use logical operators such as AND, OR, NOT, XOR, and ->.
Enter the conclusion you want tested against the premises.
Submit the form to generate the truth table and summary.
Review counterexamples first, because they prove invalidity immediately.
Use CSV export for spreadsheets and PDF export for sharing.

FAQs

1. What does this calculator actually test?

It tests whether a conclusion logically follows from the entered premises. The tool checks every possible truth assignment and looks for counterexamples where premises are true but the conclusion is false.

2. What makes an argument valid here?

An argument is valid when no counterexample exists. That means every row satisfying all premises also satisfies the conclusion. Validity depends on logical structure, not whether statements are factually true in real life.

3. Why can premises be false on many rows?

A truth table explores all possible cases. Many rows will not satisfy your premises. Those rows do not affect validity, because only rows where all premises are true can support or refute the conclusion.

4. What does vacuously valid mean?

It means your premises never become true together on any assignment. Because there is no case with true premises and false conclusion, the argument counts as logically valid, though it may not be practically informative.

5. Which operators can I use?

You can use AND, OR, NOT, XOR, implication with -> or =>, and equivalence with <-> or IFF. Parentheses help group expressions and make complex reasoning much easier to test accurately.

6. Can I use full words as variables?

This version is designed for single-letter variables like P, Q, and R. That keeps parsing reliable and truth tables readable. You can still represent real statements by mapping each one to a letter.

7. Why is there a variable limit?

Truth tables grow exponentially. With n variables, the tool must evaluate 2^n assignments. Limiting variables keeps the analysis fast, readable, and practical for browser-based review and exporting.

8. When should I export CSV or PDF?

Use CSV when you want to sort, filter, or archive truth-table rows in spreadsheet software. Use PDF when you need a shareable report for students, teachers, team reviews, or printed study material.