Summary of Equivalence Rules
| Double Negation
(DN) |
|
| p ≡ ~~p | |
| Contraposition (CONTRA) |
|
| (p ⊃ q) ≡ (~q ⊃ ~p) | |
| Repetition (REP) |
|
| p ≡ (p v p) | |
| p ≡ (p & p) |
| Commutation (COM) |
|
| (p & q) ≡ (q & p) | |
| (p v q) ≡ (q v p) |
| DeMorgan (DEM) |
|
| ~(p v q) ≡ (~p & ~q) | |
| ~(p & q) ≡ (~p v ~q) |
| Association (ASSOC) |
|
| ((p & q) & r) ≡ (p & (q & r)) | |
| ((p v q) v r) ≡ (p v (q v r)) |
| Biconditional Exchange (BE) |
|
| (p ≡ q) ≡ [(p ⊃ q) & (q ⊃ p)] | |
| Conditional Exchange (CE) |
|
| (p ⊃ q) ≡ (~p v q) | |
| Exportation (EXPORT) |
|
| (p & q) ⊃ r) ≡ ((p ⊃ (q ⊃ r)) | |
| Distribution (DIST) |
|
| (p & (q v r) ≡ (p & q) v (p & r) | |
| (p v (q & r) ≡ (p v q) & (p v r) |
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