Fomal Logic Propositional Logic 20 questions Need Answered

Dec 2nd, 2014
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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)

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


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