Disjunctief Syllogisme

Of/of-redenering: Of A of B, niet A, dus B.

Leren

Of/of-redenering: Of A of B, niet A, dus 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.

Zo herkent u het

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

Veelgemaakte fouten

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

Stapsgewijze uitwerking

Het antwoord is 42 of 56. Het antwoord is niet 42. Wat concluderen we?

Identificeer de disjunctie: 'Of 42 of 56'
Eén optie wordt uitgesloten: 'Niet 42'
Pas Disjunctief Syllogisme toe: als P onwaar, moet Q waar zijn
Concludeer: Het antwoord is 56

Antwoord: The answer is 56

Oefenadvies

Logische Deductie