Chapter 7 Pt. 1

Consider the following premises of a natural deduction proof in propositional logic. 1.~(F • N) ∨ ~(F • N)2.F • N3.Q ⊃ (F • N) Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

~(F • N) [1, Taut]

Consider the following premises of a natural deduction proof in propositional logic. 1.~N2.~(R • I)3.(N ∨ G) ⊃ (R • I) Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

~(N ∨ G) [2, 3, MT]

Consider the following premises of a natural deduction proof in propositional logic. 1.M ∨ ~P2.(M ⊃ ~B) • (~P ⊃ F)3.~P ⊃ E Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

~B ∨ F [1, 2, CD]

Consider the following premises of a natural deduction proof in propositional logic. 1.~~G2.~(S • ~P)3.(S • ~P) ∨ ~G Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

~G [2, 3, DS]

Consider the following premises of a natural deduction proof in propositional logic. 1.H2.N ∨ ~H3.(N ∨ ~H) ⊃ ~P Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

~P [2, 3, MP]

Consider the following premises of a natural deduction proof in propositional logic. 1.(S ∨ C) ⊃ R2.E • (S ∨ C)3.E ∨ (~S ∨ ~C) Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

(E ∨ ~S) ∨ ~C [3, Assoc]

Consider the following premises of a natural deduction proof in propositional logic. 1.A ⊃ (L • M)2.M ⊃ D3.~(L • M) Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

(M ⊃ D) ∨ E [2, Add]

Consider the following premises of a natural deduction proof in propositional logic. 1.~F ∨ ~F2.Q ≡ A3.~(Q ≡ A) ∨ F Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

(Q ≡ A) ⊃ F [3, Impl]

Consider the following premises of a natural deduction proof in propositional logic. 1.(H ⊃ ~D) • (R ⊃ ~D)2.R ∨ H3.R Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

(R ⊃ ~D) • (H ⊃ ~D) [1, Com]

Consider the following premises of a natural deduction proof in propositional logic. 1.~(~H • ~K)2.(H • ~K) ∨ (H • ~N)3.(H ⊃ ~K) • (K ⊃ ~H) Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

H • (~K ∨ ~N) [2, Dist]

Consider the following premises of a natural deduction proof in propositional logic. 1.E • ~R2.J ⊃ ~(E • ~R)3.R ⊃ (~E • ~E) Select the conclusion that follows in a single step from the given premises. (Hint: Begin by examining the answers.)

J ⊃ (~E ∨ ~~R) [2, DM]