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8 Cards in this Set

  • Front
  • Back

Law of Detachment


Law of Reasoning


Modus Ponens

p → q


p


---------


∴ q




[(p → q) ∧ p] → q

Contrapositive Reasoning


Modus Tollens

p → q


¬q


---------


∴ ¬p



[(p → q) ∧ ¬q] → ¬p

Transitive Reasoning


Hypothetical Syllogism

p → q


q → r


---------


∴ p → r




[(p → q) ∧ (q → r)] → (p → r)

Disjunctive Syllogism

p ∨ q


¬p


--------


∴ q






[(p ∨ q) ∧ ¬p] → q

Addition

p


----------


∴ p ∨ q




p → (p ∨ q)

Conjunction

p


q


----------


∴ p q



(p q) → (p ∧ q)

Simplificiation

p ∧ q


--------


∴ p




(p ∧ q) → p

Resolution

p ∨ q


¬p ∨ r


---------


∴ q ∨ r



[(p ∨ q) ∧ (¬p ∨ r)] → (q ∨ r)