Sillogismo Disgiuntivo

Ragionamento 'o/o': O A o B, non A, quindi B.

Impara

Ragionamento 'o/o': O A o B, non A, quindi 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.

Come riconoscerlo

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

Errori comuni

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

Soluzione passo per passo

La risposta è 42 o 56. La risposta non è 42. Cosa concludiamo?

Identifica la disgiunzione: 'O 42 o 56'
Un'opzione è esclusa: 'Non 42'
Applica Sillogismo Disgiuntivo: se P è falso, Q deve essere vero
Concludi: La risposta è 56

Risposta: The answer is 56

Indicazioni per la pratica

Deduzione Logica