Syllogisme Hypothétique

Apprendre

Raisonnement en chaîne : Si A alors B, Si B alors C, donc Si A alors C.

Hypothetical Syllogism (also called Chain Reasoning or Hypothetical Chain) allows us to link conditional statements together. If we know that A implies B, and B implies C, we can conclude that A implies C. This rule is essential for building chains of reasoning and is widely used in mathematical proofs and everyday logic.

P → Q, Q → R ⊢ P → R

• If it rains, the streets get wet. If the streets get wet, traffic slows down. Therefore, if it rains, traffic slows down.
• If you exercise regularly, you build stamina. If you build stamina, you can run longer. Therefore, if you exercise regularly, you can run longer.
• If a shape is a square, it is a rectangle. If a shape is a rectangle, it is a quadrilateral. Therefore, if a shape is a square, it is a quadrilateral.

Comment le reconnaître

• Look for two 'If...then...' statements (conditionals)
• The consequent of the first should match the antecedent of the second
• The conclusion links the first antecedent to the last consequent

Erreurs fréquentes

• Reversing the chain: 'If A then B, If C then B' does NOT give 'If A then C'
• The middle terms must match exactly for the chain to be valid

Conseils de pratique

Déduction Logique