Laws of Propositional Logic
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Last updated 9:28 PM on 1/23/26
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14 Terms
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Identity
p ∧ T ≡ p; p ∨ F ≡ p
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Domination
p ∨ T ≡ T; p ∧ F ≡ F
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Idempotent
p ∧ p ≡ p; p ∨ p ≡ p
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Double Negation
¬¬p ≡ p
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Commutativity
p ∧ q ≡ q ∧ p; p ∨ q ≡ q ∨ p
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Associativity
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r); (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
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Distributive Laws
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r); p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
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DeMorgan's Laws
¬(p ∧ q) ≡ (¬p ∨ ¬q); ¬(p ∨ q) ≡ (¬p ∧ ¬q)
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Absorption
p ∨ (p ∧ q) ≡ p; p ∧ (p ∨ q) ≡ p
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Tautology
p ∨ ¬p ≡ T
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Contradiction
p ∧ ¬p ≡ F
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Contrapositive
p ⇒ q ≡ ¬q ⇒ ¬p
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Conditional Disjunction Equivalence
p ⇒ q ≡ ¬p ∨ q
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Biconditional
p ⇔ q ≡ (p ⇒ q) ∧ (q ⇒ p)
Note 
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