Fomal Logic Propositional Logic

Question description

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

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