# 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)

 ∼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

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

 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) 