Contropositivo

Equivalenza logica: 'Se A allora B' è equivalente a 'Se non B allora non A'.

Impara

Equivalenza logica: 'Se A allora B' è equivalente a 'Se non B allora non A'.

The Contrapositive is a logically equivalent form of a conditional statement. For any conditional 'If A then B', its contrapositive 'If not B then not A' has exactly the same truth value. This equivalence is fundamental in mathematics, particularly in proof by contrapositive, where proving the contrapositive is often easier than proving the original statement directly.

P → Q ≡ ¬Q → ¬P

'If it is a dog, then it is an animal' is equivalent to 'If it is not an animal, then it is not a dog'
'If n² is even, then n is even' is equivalent to 'If n is odd, then n² is odd'
'If you pass the exam, you studied' is equivalent to 'If you did not study, you did not pass the exam'

Come riconoscerlo

Start with an 'If A then B' statement
Negate both parts: A becomes 'not A', B becomes 'not B'
Swap their positions: 'If not B then not A'

Errori comuni

Confusing contrapositive with converse: 'If B then A' is the converse, NOT equivalent to the original
Confusing contrapositive with inverse: 'If not A then not B' is the inverse, NOT equivalent to the original
Only the contrapositive preserves logical equivalence

Soluzione passo per passo

Trova il contropositivo di: 'Se è un cane, allora è un animale'

Identifica l'originale: 'Se cane → animale'
Nega entrambe le parti: 'non cane' e 'non animale'
Scambia le posizioni: 'Se non animale → non cane'
Enuncia il contropositivo: 'Se non è un animale, allora non è un cane'

Risposta: If it is not an animal, then it is not a dog

Indicazioni per la pratica

Deduzione Logica