Experiment
Formal Logic
Build propositional logic expressions and see their truth tables generated instantly. Use variables (P, Q, R, S), connectives (∧, ∨, ¬, →, ↔), and parentheses. The expression tree reveals structure; the truth table reveals meaning.
Truth table
Expression tree
Inference rules reference
Modus Ponens
P → Q, P ⊢ Q
Modus Tollens
P → Q, ¬Q ⊢ ¬P
Hypothetical Syllogism
P → Q, Q → R ⊢ P → R
Disjunctive Syllogism
P ∨ Q, ¬P ⊢ Q
De Morgan (1)
¬(P ∧ Q) ≡ ¬P ∨ ¬Q
De Morgan (2)
¬(P ∨ Q) ≡ ¬P ∧ ¬Q