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