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18 Rules of Inference/Replacement for
Propositional Logic Proofs Questions
with Correct Answers
Modus Ponens (MP) - ANSWERSp ⊃ q p
q Modus Tollens (MT) - ANSWERSp ⊃ q ~q
~p Hypothetical Syllogism (HS) - ANSWERSp ⊃ q q ⊃ r
p ⊃ r Disjunctive Syllogism (DS) - ANSWERSp v q ~p
q Constructive Dilemma (CD) - ANSWERS(p ⊃ q) • (r ⊃ s) p v r
q v s Simplification (Simp) - ANSWERSp • q
p Conjunction (Conj) - ANSWERSp q
p • q Addition (Add) - ANSWERSp
p v q De Morgan's Rule (DM) - ANSWERS~(p • q) :: (~p v ~q) ~(p v q) :: (~p • ~q) Commutativity (Com) - ANSWERS(p v q) :: (q v p) (p • q) :: (q • p) Associativity (Assoc) - ANSWERS[p v (q v r)] :: [(p v q) v r] [p • (q • r)] :: [(p • q) • r] Distribution (Dist) - ANSWERS[p • (q v r)] :: [(p • q) v (p • r)] [p v (q • r)] :: [(p v q) • (p v r)] Double Negation (DN) - ANSWERSp :: ~~p Transposition (Trans) - ANSWERS(p ⊃ q) :: (~q ⊃ ~p) Material Implication (Impl) - ANSWERS(p ⊃ q) :: (~p v q) Material Equivalence (Equiv) - ANSWERS(p ≡ q) :: [(p ⊃ q) • (q ⊃ p)] (p ≡ q) :: [(p • q) v (~p • ~q)] Exportation (Exp) - ANSWERS[(p • q) ⊃ r] :: [p ⊃ (q ⊃ r)] Tautology (Taut) - ANSWERSp :: (p v p) p :: (p • p)
