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Propositional Logic Evaluator Calculator

Work out propositional logic evaluator instantly with clear inputs, formula shown and shareable results.

About Propositional Logic Evaluator Calculator

A propositional formula is evaluated by substituting truth values for the variables. Checking all 2ⁿ rows determines whether it is a tautology, a contradiction, or merely contingent — the basis of formal proof checking.

Formulas

Modus ponens

((P → Q) ∧ P) → Q is a tautology

De Morgan

¬(P ∧ Q) ↔ (¬P ∨ ¬Q)

Worked example

With the default values below, Propositional Logic Evaluator Calculator returns Classification of Tautology — true in every case. Change any input above and every figure here is recalculated in your browser.

Inputs used

Formulaone of (P → Q) ∧ P → Q (modus ponens), (P → Q) ∧ ¬Q → ¬P (modus tollens), ¬(P ∧ Q) ↔ ¬P ∨ ¬Q (De Morgan), P ∨ ¬P (excluded middle)
(P → Q) ∧ P → Q (modus ponens)
Value of Paccepts 0–1
1
Value of Qaccepts 0–1
1

Results

Classification
Tautology — true in every case
Value at your P and Q
True
Rows that come out true
4
Total rows
4

Step by step

  1. 1Values used
  2. 2Modus ponens
  3. 3De Morgan
  4. 4Classification= Tautology — true in every case
  5. 5Value at your P and Q= True
  6. 6Rows that come out true= 4
  7. 7Total rows= 4

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is modus ponens a tautology?

Yes, it is true in all four rows, which is why it is a valid rule of inference.

What makes a formula contingent?

It is true for some assignments and false for others, so it carries genuine information about the world.

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