Reference no: EM13725308

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