SD+ Derivation Rules
All the Derivation Rules of SD and
Rules of Inference
Modus Tollens (MT)
P⊃Q | |
∼Q | |
⊳ | ∼P |
Hypothetical Syllogism (HS)
P⊃Q | |
Q⊃R | |
⊳ | P⊃R |
Disjunctive Syllogism (DS)
P∨Q | |
∼P | |
⊳ | Q |
P∨Q | |
∼Q | |
⊳ | P |
Rules of Replacement
Commutation (Com)
P&Q⊲⊳Q&P
P∨Q⊲⊳Q∨P
Association (Assoc)
P&(Q&R)⊲⊳(P&Q)&R
P∨(Q∨R)⊲⊳(P∨Q)∨R
Implication (Impl)
P⊃Q⊲⊳∼P∨Q
Double Negation (DN)
P⊲⊳∼∼P
De Morgan (DeM)
∼(P&Q)⊲⊳∼P∨∼Q
∼(P∨Q)⊲⊳∼P&∼Q
Idempotence (Idem)
P⊲⊳P&P
P⊲⊳P∨P
Transposition (Trans)
P⊃Q⊲⊳∼Q⊃∼P
Exportation (Exp)
P⊃(Q⊃R)⊲⊳(P&Q)⊃R
Distribution (Dist)
P&(Q∨R)⊲⊳(P&Q)∨(P&R)
P∨(Q&R)⊲⊳(P∨Q)&(P∨R)
P∨(Q&R)⊲⊳(P∨Q)&(P∨R)
Equivalence (Equiv)
P≡Q⊲⊳(P⊃Q)&(Q⊃P)
P≡Q⊲⊳(P&Q)∨(∼P&∼Q)