Work out propositional logic evaluator instantly with clear inputs, formula shown and shareable results.
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.
Modus ponens
((P → Q) ∧ P) → Q is a tautology
De Morgan
¬(P ∧ Q) ↔ (¬P ∨ ¬Q)
Yes, it is true in all four rows, which is why it is a valid rule of inference.
It is true for some assignments and false for others, so it carries genuine information about the world.