1. Natural Deduction
Hurley, Logic 7.1

2. 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

3. 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

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

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

6. Practice Finding Proof Steps
T → U
R → S / R → U
S → U ,2 HS
R → U ,4 HS

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

8. 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) ,2, DS
C → D ,5, MP
C → G ,6, HS

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

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

11. Practice Finding Proof Steps
(L Ξ N) → C
(L Ξ N) v (P → ~E)
~E → C
~C / ~P
~~E ,4, MT
~(L Ξ N) ,4, MT
P → ~E ,6, DS
~P ,7, MT