Natural Deduction Hurley, Logic 7.1

Our First 4 Argument Forms Modus Ponens: p → q p _______ q Modus Tollens ~q ~p Hypothetical Syllogism: p → q q → r _______ p → r Disjunctive Syllogism p v q ~p q Remember that p, q, and r stand for any well-formed formula, no matter how complex. For instance, below is an example of disjunctive syllogism: ~(K v J) v ~B ~~(K v J) __________ ~B

Practice Finding Proof Steps 1. A → B 2. ~A → (C v D) 3. ~B 4. ~C / D 5. ~A 1,3 MT 6. C v D 2,5 MP 7. D 4,6 DS

Practice Finding Proof Steps F → G F v H ~G H → (G → I) / F → I ~ F 1,3 MT H 2,5 DS G → I 4,6 MP F → I 1,7 HS

Practice Finding Proof Steps ~J J v K K → L / L K 1,2 DS L 3,4 MP

Practice Finding Proof Steps T → U R → S / R → U S → U 1,2 HS R → U 3,4 HS

Practice Finding Proof Steps E → (K → L) (Example from Hurley 12th edition) F → (L → M) G v E ~G F / K → M L → M 2,5 MP E 3,4 DS K → L 1,7 MP K → M 6,8 HS

Practice Finding Proof Steps ~(A ● B) v [~(E ● F) → (C → D)] (Example from Hurley 11th edition) ~~(A ● B) ~(E ● F) D → G / C → G ~(E ● F) → (C → D) 1,2, DS C → D 3,5, MP C → G 4,6, HS

Practice Finding Proof Steps G → [~O → (G → D)] O v G ~O / D G 2,3, DS ~O → (G → D) 1,4, MP G → D 3,5, MP D 4,6, MP

Practice Finding Proof Steps ~M v (B v ~T) B → W ~~M ~W / ~T B v ~T 1,3, DS ~B 2,4, MT ~T 5,6, DS

Practice Finding Proof Steps (L Ξ N) → C (L Ξ N) v (P → ~E) ~E → C ~C / ~P ~~E 3,4, MT ~(L Ξ N) 1,4, MT P → ~E 2,6, DS ~P 5,7, MT