VRRP: Increasing Reliability and Failover with the Virtual Router Redundance Protocol

E.2. Logical Laws and Equivalences Used in the Discussions

Propositional Logic

(2) p → q ≡ ¬q → ¬p	Transposition
(3) p ↔ q ≡ ¬p ↔ ¬q	Negating Biconditionals
(4) (p → q) ∧ (q → p) ≡ p ↔ q	Biconditional and Conjunction
(5) p ↔ q ≡ (p ∧ q ) ∨ (¬p ∧¬q)	Biconditional and Disjunction
(6) p → q ≡ ¬p ∨ q	Conditional and Disjunction
(7) ¬ (p ∧ q) ≡ ¬p ∨ ¬q	DeMorgan Law
(8) ¬ (p ∨ q) ≡ ¬p ∧ ¬q	DeMorgan Law
(9) ¬¬p ≡ p	Double Negation
(10) p → q ≡ ¬(p ∧ ¬q)	Conditional and Negated Conjunction
(11) p ∨ q ≡ ¬(¬p ∧ ¬q)	DeMorgan with Double Negation
(12) p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)	Conjunctive Distribution
(13) p ∧ q ≡ p ∧ q	Commutativity of Conjunction
(14) p ∨ (p ∧ q) ≡ p	Special Idempotent

First-Order Predicate Logic

(15) ¬∀x F(x) ≡ ∨ ∃x¬F(x)

Universal ...