Propositional Logic Worksheet Page 17
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21LOGICAL IDENTITIES
idempotence of ∧
P ≡ P ∧ P
idempotence of ∨
P ≡ P ∨ P
commutativity of ∨
P ∨ Q ≡ Q ∨ P
commutativity of ∧
P ∧ Q ≡ Q ∧ P
(P ∨ Q) ∨ R ≡ P ∨ (Q ∨ R)
associativity of ∨
(P ∧ Q) ∧ R ≡ P ∧ (Q ∧ R)
associativity of ∧
DeMorgan’s Laws
¬(P ∨ Q) ≡ ¬P ∧ ¬Q
¬(P ∧ Q) ≡ ¬P ∨ ¬Q
P ∧ (Q ∨ R) ≡ (P ∧ Q) ∨ (P ∧ R) distributivity of ∧ over ∨
P ∨ (Q ∧ R) ≡ (P ∨ Q) ∧ (P ∨ R) distributivity of ∨ over ∧
domination laws
P ∨ T ≡ T
P ∧ F ≡ F
identity laws
P ∧ T ≡ P
P ∨ F ≡ P
negation laws
P ∨ ¬P ≡ T
P ∧ ¬P ≡ F
¬(¬P ) ≡ P
double negation law
P ∨ (P ∧ Q) ≡ P
absorption laws
P ∧ (P ∨ Q) ≡ P
implication
P → Q ≡ ¬P ∨ Q
contrapositive
P → Q ≡ ¬Q → ¬P
P ↔ Q ≡ [(P → Q) ∧ (Q → P )]
equivalence
[(P ∧ Q) → R] ≡ [P → (Q → R)] exportation
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