Logical Equivalences

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# Logical Equivalences - PowerPoint PPT Presentation

Law. Name. P  P  T P  P  F. Excluded middle law Contradiction law. P  F  P P  T  P. Identity laws. P  T  T P  F  F. Domination laws. P  P  P P  P  P. Idempotent laws. (P)  P. Double-negation law. Logical Equivalences. P  Q  Q  P P  Q  Q  P.

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## Logical Equivalences

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1. Law Name P  P  T P  P  F Excluded middle law Contradiction law P  F  P P  T  P Identity laws P  T  T P  F  F Domination laws P  P  P P  P  P Idempotent laws (P)  P Double-negation law Logical Equivalences

2. P  Q  Q P P  Q  Q  P Commutative laws (P  Q)  R  P  (Q  R) (P  Q)  R  P  (Q  R) Associative laws (P  Q)  (P  R)  P  (Q  R) (P  Q)  (P  R)  P  (Q  R) Distributive laws (P  Q)  P  Q (P  Q)  P  Q De Morgan’s laws P  (P  Q)  P P  (P  Q)  P P  Q  P  Q P  Q (P  Q)  (Q  P) Absorption laws Implication law Bi-conditional law

3. Basic Set Identities

4. Basic Set Identities (continued…)

5. Main Rules of Inference