Advanced Modus Tollens Calculator

Calculator

Statement P

Example: The number is divisible by 4.

Statement Q

Example: The number is even.

Truth value of P

Truth value of Q

Premise 1

Premise 2

Example Data Table

This sample shows a classic case where modus tollens applies successfully.

P statement	Q statement	P	Q	P -> Q	Not Q	Not P	Outcome
The number is divisible by 4	The number is even	False	False	True	True	True	Modus tollens applies

Formula Used

Core inference rule: (P -> Q) and (Not Q) therefore (Not P)

Implication test: P -> Q is equivalent to (Not P) or Q

Modus tollens is a valid deductive rule. The calculator first evaluates the implication P -> Q using the logical identity (Not P) or Q. It then checks whether Not Q is true. If both premises hold, the derived conclusion Not P must also hold.

This calculator also builds the full truth table. That table confirms the argument form stays valid because every row satisfying both premises also makes the conclusion true.

How to Use This Calculator

Enter a clear statement for proposition P.
Enter a related statement for proposition Q.
Select the truth value you want to test for P.
Select the truth value you want to test for Q.
Press Submit to evaluate the implication and conclusion.
Review the summary, scenario status, and truth table.
Use the export buttons to save the current result.

FAQs

1. What does modus tollens mean?

It is a valid deductive rule. From “If P, then Q” and “Not Q,” you can infer “Not P.”

2. Is modus tollens always logically valid?

Yes. The argument form is always valid. If both premises are true, the conclusion must be true as well.

3. Why does the calculator ask for truth values?

Truth values let you test a specific scenario. They show whether your chosen case actually satisfies the premises of the rule.

4. What if both premises are not satisfied?

The rule remains valid, but your selected row does not support an active modus tollens step. The calculator reports that difference clearly.

5. What is the implication formula used here?

The calculator uses the equivalence P -> Q = (Not P) or Q. This makes implication testing direct and consistent.

6. Can I use natural language statements?

Yes. Enter any short statements for P and Q. The calculator converts them into a readable logical inference summary.

7. What does the truth table section show?

It lists all four possible truth combinations for P and Q. You can compare your selected scenario against every logical row.

8. What do the export buttons save?

They save your current result summary. CSV creates a spreadsheet-friendly file, while PDF produces a compact report for sharing.