Syllogisme Disjonctif

Raisonnement 'ou/ou' : Soit A soit B, pas A, donc B.

Apprendre

Raisonnement 'ou/ou' : Soit A soit B, pas A, donc B.

Disjunctive Syllogism is a rule of inference that eliminates alternatives. Given that 'Either A or B' is true (at least one must hold), and knowing that A is false, we can conclude that B must be true. This is also called 'process of elimination' and is fundamental to decision-making and proof by cases.

P ∨ Q, ¬P ⊢ Q

Either the package was delivered or it was lost. It was not delivered. Therefore, it was lost.
Either the answer is 42 or 56. The answer is not 42. Therefore, the answer is 56.
Either John took the bus or he walked. John did not take the bus. Therefore, John walked.

Comment le reconnaître

Look for an 'Either...or...' statement (disjunction)
One of the options is ruled out (negated)
The conclusion affirms the remaining option

Erreurs fréquentes

Assuming 'Either A or B' means exactly one is true (exclusive or). In logic, 'or' typically allows both to be true
Affirming one disjunct does not eliminate the other: 'Either A or B, A is true' does NOT mean B is false

Résolution étape par étape

La réponse est 42 ou 56. La réponse n'est pas 42. Que conclure ?

Identifiez la disjonction : 'Soit 42 soit 56'
Une option est éliminée : 'Pas 42'
Appliquez le Syllogisme Disjonctif : si P est faux, Q doit être vrai
Concluez : La réponse est 56

Réponse: The answer is 56

Conseils de pratique

Déduction Logique