Fomal Logic Propositional Logic, philosophy homework help
Question 1
Select the conclusion that follows in
a single step from the given premises:
1. ~R≡ ~R
2. N • ~T
3. R ⊃ ~(N • ~T)
∼T
2, Simp
(N •∼T)⊃∼R
3, Trans
∼R
2, 3, MT
R⊃(∼N∨∼∼T) 3, DM
∼R
1, Taut
Question 2
Select the conclusion that follows in
a single step from the given premises:
1. N ∨ C
2. (N ∨ C) ⊃ (F ⊃ C)
3. ~C
F⊃C
1, 2, MP
N 1, 3, DS
∼F
2, 3, MT
∼N
1, 3, MT
∼C
•
R
3, Add
Question 3
Select the conclusion that follows in
a single step from the given premises:
1. A
2. (A ⊃ ~T) ⊃ ~G
3. Q ⊃ (A ⊃ ~T)
Q⊃(T⊃∼A)
3, Trans
(Q⊃A)⊃∼T
3, Assoc
A⊃(∼T
•∼G)
2, Exp
∼T
1, 3, MP
Q⊃∼G
2, 3, HS
Question 4
Select the conclusion that follows in
a single step from the given premises:
1. D ⊃ H
2. ~D
3. ~(D ∨ S)
∼H
1, 2, MT
∼D∨(D⊃H)
2, Add
H⊃D
1, Com
S 2, 3, DS
∼D∨∼S
3, DM
Question 5
Select the conclusion that follows in
a single step from the given premises:
1. ~U ⊃ (S • K)
2. R ⊃ (~U • ~U)
3. S ≡ ~U
(∼U • S)⊃K
1, Exp
R⊃U
2, DN
R⊃∼U
2, Taut
R⊃(S •
K)
1, 2, HS
(S⊃U) • (∼U⊃∼S) 3, Equiv
Question 6
Select the conclusion that follows in
a single step from the given premises:
1. P • (~H ∨ D)
2. ~(~P • ~H)
3. (P ⊃ ~H) • (~P ⊃ H)
P ≡ ∼H
3, Equiv
∼H∨D
1, Simp
(P •∼H)∨D
1, Assoc
P • (H⊃D)
1, Impl
P •
H
2, DN
Question 7
Select the conclusion that follows in
a single step from the given premises:
1. ~(Q • ~S)
2. ~F ⊃ (Q • ~S)
3. H ∨(Q • ~S)
(H • Q)∨(H •∼S) 3, Dist
∼Q∨S
1, DM
F 1, 2, MT
H
1, 3, DS
~~F 1, 2, MT
Question 8
Select the conclusion that follows in
a single step from the given premises:
1. Q ⊃ (A ∨ ~T)
2. T
3. A ∨ ~T
Q⊃(∼∼A∨∼T) 1, DN
(A∨∼T)⊃Q
1, Com
(Q⊃A)∨∼T
1, Assoc
Q 1, 3, MP
A 2, 3, DS
Question 9
Select the conclusion that follows in
a single step from the given premises:
1. (J • ~N) ∨ T
2. ~(J • ~N)
3. ~T
T 1, 2, DS
∼J∨N
2, DM
J •∼N
1, 3, DS
J • (∼N∨T)
1, Assoc
∼J 2, Simp
Question 10
Select the conclusion that follows in
a single step from the given premises:
1. (K • ~T) ∨ (K • ~H)
2. ~M ⊃ (K • ~H)
3. ~(K • ~H)
∼K∨H
3, DM
K •∼T
1, 3, DS
K • (∼T∨∼H)
1, Dist
M
2, 3, MT
(∼M • K)⊃∼H
2, Exp
Question 11
Select the conclusion that follows in
a single step from the given premises:
1. ~I ∨ ~~B
2. M ⊃ ~I
3. I
M⊃∼∼B
1, 2, HS
∼∼B
1, 3, DS
∼M
2, 3, MT
∼I⊃M
2, Com
∼(I •∼B)
1, DM
Question 12
Select the conclusion that follows in
a single step from the given premises:
1. A
2. G ⊃ (A ⊃ ~L)
3. ~A ∨ ~G
A∨G
3, DN
(G⊃A)⊃∼L
2, Assoc
∼L
1, 2, MP
∼G
1, 3, DS
G⊃(∼∼L⊃∼A) 2,
Trans
Question 13
Select the conclusion that follows in
a single step from the given premises:
1. (S • ~J) ∨ (~S • ~~J)
2. S ∨ ~S
3. ~J ⊃ P
S 2, Taut
∼J∨∼∼J
1, 2, CD
S ≡ ∼J
1, Equiv
J∨P
3, Impl
∼P⊃J
3, Trans
Select
the conclusion that follows in a single step from the given premises:
1. (S ⊃ ~F) • (~F ⊃ B)
2. S ∨ ~F
3. ~F
S⊃B
1, HS
∼F∨B
1, 2, CD
S
2, 3, DS
B
1, 3, MP
∼S
1, 3, MT
Question 15
Select the conclusion that follows in
a single step from the given premises:
1. ~M ⊃ S
2. ~M
3. (M ∨ H) ∨ ~S
H 2, 3, DS
M∨H
3, Simp
M∨(H∨∼S)
3, Assoc
∼S
1, 2, MP
M∨S
1, Impl
Question 16
Select the conclusion that follows in
a single step from the given premises:
1. G • ~A
2. K ⊃ (G • ~A)
3. G ⊃ M
(K⊃G )⊃∼A 2, Exp
K⊃(∼A
•
G)
2, Com
(K⊃G) •∼A
2, Assoc
K
1, 2, MP
M
1, 3, MP
Question 17
Select the conclusion that follows in
a single step from the given premises:
1. ~E ⊃ P
2. ~P
3. ~(P ∨ ~H)
∼H
2, 3, DS
∼P •∼(P∨∼H) 2, 3,
Conj
∼P • H
3, DM
E 1, 2, MT
∼P⊃E
1, Trans
Question 18
Select the conclusion that follows in
a single step from the given premises:
1. N ≡ R
2. (N • ~R) ⊃ C
3. N
(N⊃R)∨(R⊃N) 1, Equiv
N • (∼R⊃C)
2, Assoc
C⊃(N •∼R)
2, Com
N⊃(∼R⊃C)
2, Exp
R 1, 3, MP
Question 19
Select the conclusion that follows in
a single step from the given premises:
1. N
2. R ⊃ ~N
3. ~C • (T ⊃ R)
∼C
3, Simp
T⊃∼N
2, 3, HS
(∼C • T)⊃R
3, Assoc
∼R
1, 2, MT
N⊃∼R
2, Trans
Question 20
Select the conclusion that follows in
a single step from the given premises:
1. ~N • ~F
2. K ⊃ (N • F)
3. U ∨ (K • ~N)
∼K
1, 2, MT
(U∨K) •∼N
3, Assoc
(K • N)⊃F
2, Exp
(U∨K) • (U∨∼N) 3, Dist
∼(N •
F)
1, DM