Propositional Equivalence

Propositional-Equivalence

Tautology

  • Tautology(恒真)
  • contradiction(矛盾)
  • contingency(偶然)

Logical Equivalence

  • Two propositions (P,Q) are equivalent if the proposition \(P≡Q\)
    • If two propositions are equivalent, they must have the same truth table.

Laws

  • Identity(同一) laws
    • $p\wedge T \equiv p$
    • $p\vee F \equiv p$
  • Domination(支配) laws
    • $p \vee T \equiv T$
    • $p \wedge F \equiv F$
  • Idempotent (幂等) laws
    • $p\vee p\equiv p$
    • $p\wedge p\equiv p$
  • Double negation laws
    • $\neg(\neg p)\equiv p$

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