1. INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. Q ⊃ (H • ∼F)
2. ∼(Q • ∼M)
3. ∼G ⊃ (Q • ∼M)
G ∨∼(Q • M) 2, Add
Q 2, Simp
∼Q ∨∼∼M 2, DM
Q ⊃∼(∼H ∨ F) 1, DM
G 2, 3, MT
1. INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. F ⊃ J
2. A ⊃ (F • J)
3. A • (Q ∨ N)
J ⊃ F 1, Com
A • (N ∨ Q) 3, Com
A ⊃ J 1, 2, HS
(A ⊃ F) • (A ⊃ J) 2, Dist
(A • Q) ∨ N 3, Assoc
1. INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. (C • ∼F) ⊃ E
2. G ∨ (C • ∼F)
3. ∼(C • ∼F)
G ⊃ E 1, 2, HS
C 1, Simp
C ⊃ (∼F ⊃ E) 1, Exp
(G ∨ C) • ∼F 2, Assoc
G 2, 3, DS
1. INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. K ∨∼H
2. (K ∨∼H) ⊃ (B ⊃ J)
3. J ⊃ D
H ⊃ K 1, Impl
B ⊃ D 2, 3, HS
K 1, Simp
D ⊃ J 3, Trans
B ⊃ J 1, 2, MP
INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. R • ∼S
2. R ⊃∼(S • ∼F)
3. ∼S ⊃ (F • N)
(∼S • F) ⊃ N 3, Exp
∼S 1, Simp
F • N 1, 3, MP
R ⊃ (∼S ∨∼∼F) 2, DM
(∼S ⊃ F) • (∼S ⊃ N) 3, Dist
1. INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises.
Given the following premises:
1. ∼T ⊃ E
2. ∼K ⊃ (∼T ∨∼T)
3. M ⊃ (∼K ∨∼L)
(M ⊃∼K) ∨ L 3, Assoc
M ⊃ (K ⊃∼L) 3, Impl
M ⊃ (K ∨ L) 3, DN
∼K ⊃ T 2, Taut
∼K ⊃ E 1, 2, HS
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. N > R 2. O <> R 3. (O > R) > L / (N > O) & L
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. C 2. (C & T) > ~T 3. (C & ~T) > T / T <> ~T
Construct a regular proof to derive the conclusion of the following argument:
1. X >Y 2. (Y v ~X) > (Y > Z) / ~Z > ~X
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. (A & U) <> ~R
2. ~(~R v ~A) / ~U
INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use indirect proof:
1. (R v S) ?(H • ~G)
2. (K v R) ? (G v ~H) / ~R
INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use conditional proof:
1. N ⊃ (F • A)
2. B ⊃ (R • F) / (N ⊃ B) ⊃ (A ⊃ R)
iNSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems.
Use an ordinary proof (not conditional or indirect proof):
1. A ⊃ (Q ∨ R)
2. (R • Q) ⊃ B
3. A • ∼B / R ≡ ∼Q