Fomal Logic Propositional Logic 20 questions Need Answered
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)
Which Answer:
∼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
Which Answer:
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)
Which Answer:
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)
Which Answer:
∼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
Which Answer:
(∼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)
Which Answer:
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)
Which Answer:
(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
Which Answer:
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
Which Answer:
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)
Which Answer:
∼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
Which Answer:
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
Which Answer:
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
Which Answer:
S 2, Taut
∼J∨∼∼J 1, 2, CD
S ≡∼J 1, Equiv
J∨P 3, Impl
∼P⊃J 3, Trans
Question 14
Select the conclusion that follows in a single step
from the given premises:
1. (S ⊃ ~F) • (~F ⊃ B)
2. S ∨ ~F
3. ~F
Which Answer:
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
Which Answer:
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
Which Answer:
(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)
Which Answer:
∼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
Which Answer:
(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)
Which Answer:
∼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)
Which Answer:
∼K 1, 2, MT
(U∨K) •∼N 3, Assoc
(K • N)⊃F 2, Exp
(U∨K) • (U∨∼N) 3, Dist
∼(N • F) 1, DM