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 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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