Tutors Answer Your Questions about Proofs (FREE)
Question 1210239: 1. use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
~(T v U), S, R ≡ ~S /.: ~(U v R)
2. use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
S v (~R • T), R ⊃ ~S /.: ~R
3. use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
S v (T ⊃ R), S ⊃ T, ~(T ⊃ R) /.: T
First, copy the argument above and paste it into the text box. Second, using the spacebar, set up your proof into two columns. Third, type or copy and paste symbols as required to complete your proof. For an assumed premise, use '→' before the line number. For the vertical line of a subproof, use '|' before the line number. For the horizontal line of a subproof, simply use the underline edit button (click on the "Show more buttons" button to see it). You can use the spacebar to align everything near perfectly. Don't worry about the double space between lines
Click here to see answer by Edwin McCravy(20067)   |
Question 1210240: 1. use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
~(T v U), S, R ≡ ~S /.: ~(U v R)
2. use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
S v (~R • T), R ⊃ ~S /.: ~R
3. use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
S v (T ⊃ R), S ⊃ T, ~(T ⊃ R) /.: T
First, copy the argument above and paste it into the text box. Second, using the spacebar, set up your proof into two columns. Third, type or copy and paste symbols as required to complete your proof. For an assumed premise, use '→' before the line number. For the vertical line of a subproof, use '|' before the line number. For the horizontal line of a subproof, simply use the underline edit button (click on the "Show more buttons" button to see it). You can use the spacebar to align everything near perfectly. Don't worry about the double space between lines
Click here to see answer by Edwin McCravy(20067) |
Question 1210174: Use the quantifier negation rule together with the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof. (Complete the proof in the logic tool. See the Getting Started text for further instructions. Select the Submit button to grade your response.)
Step Argument Justification
1. ~(∃x)(Ax ⦁ ~Bx)
2. ~(∃x)(Ax ⦁ ~Cx) / (x)[Ax ⊃ (Bx ⦁ Cx)]
Click here to see answer by CPhill(1987)  |
Question 1210175: Use the quantifier negation rule together with the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof. (Complete the proof in the logic tool. See the Getting Started text for further instructions. Select the Submit button to grade your response.)
Step Argument Justification
1. (x)[(Ax ⦁ Bx) ⊃ Cx]
2. ~(x)(Ax ⊃ Cx) / ~(x)Bx
Click here to see answer by CPhill(1987) |
Question 1210176: Use the quantifier negation rule together with the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof. (Complete the proof in the logic tool. See the Getting Started text for further instructions. Select the Submit button to grade your response.)
Step Argument Justification
1. (∃x)Ax ⊃ [(∃x)Bx ∨ (x)Cx]
2. (∃x)(Ax ⦁ ~Cx)
3. ~(x)Cx ⊃ [(x)Fx ⊃ (x)~Bx] / (∃x)~Fx
Click here to see answer by CPhill(1987) |
Question 1171517: For any TFL sentences 𝛼 and 𝛽 that are logically equivalent (i.e., whose truth values agree on every valuation of their sentence letters), does the following entailment hold:
𝛽 → 𝛼, 𝛼 ∨ 𝛽 ⊨ 𝛼 ∧ 𝛽
Could someone help me with this problem?
Thank you!
Click here to see answer by CPhill(1987) |
Question 1179563: I could really use some help. Thank You
INSTRUCTIONS: Use natural deduction to derive the conclusion in each problem.
Prove this using natural deduction.
NOTE: Use * for dot, v for wedge, ~ for tilde, = for triple bar (or copy and paste ≡), and > for horseshoe (or copy and paste ⊃ )
1. N ≡ F
2. ~F v ~N
3. D ⊃ N /~(F v D)
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1. M ⊃ (∼B ⊃ J)
2. B ⊃ (~M * ~M)
3. ∼J / ~M
------------------------
1. ~X ⊃ ~~O
2. ~X ⊃ A
3. ~(O * A) / X
Click here to see answer by CPhill(1987) |
Question 1179696: INSTRUCTIONS: Use natural deduction to derive the conclusion in each problem.
Prove this using natural deduction.
NOTE: Use * for dot, v for wedge, ~ for tilde, = for triple bar (or copy and paste ≡), and > for horseshoe (or copy and paste ⊃ )
1. N ≡ F
2. ~F v ~N
3. D ⊃ N ~(F v D)
1. (B ⊃ G) • (F ⊃ N)
2. ~(G * N) / ~(B * F)
1. (J • R) ⊃ H
2. (R ⊃ H) ⊃ M
3. ~(P v ~J) / M • ~P
1. (F • H) ⊃ N
2 F v S
3. H / N v S
Please any guidance on these 4 questions I'd greatly appreciate it!
Click here to see answer by CPhill(1987) |
Question 1179864: I. Use an ordinary proof (not conditional or indirect) to solve the following arguments.
1)
1. I v (N • F)
2. I ⊃ F /F
2)
1. P ⊃ ~M
2. C ⊃ M
3. ~L v C
4. (~P ⊃ ~E) • (~E ⊃ ~C)
5. P v ~P /~L
3)
1. O ⊃ (Q • N)
2. (N Ú E) ⊃ S / O ⊃ S
Click here to see answer by CPhill(1987) |
Question 1191579: You are on the island of knights and knaves, where (a) every local is either
a knight or a knave, (b) knights always tell the truth, and (c) knaves always
lie. Using a symbolic technique (truth table or natural deduction), can you
determine who is a knight and who is a knave? (10 pts. for translation, 10 pts.
for truth table/proof and verdict)
You meet three locals: Al, Bob, and Carol. Al says, “I’m a knave only
if Carol is a knight.” Bob says, “I’m a knight if Carol is.” Carol says,
“Neither Al nor Bob is a knight.”
Click here to see answer by CPhill(1987) |
Question 1191241: Please prove the following arguments (10 questions, 1 point each):
(1) P ∨ P ⊢ P
(2) P ⊢ (P → Q) → Q
(3) ∼(P & Q), P ⊢ ∼ Q
(4) P ⊢ (∼(Q → R) → ∼ P) → (∼ R → ∼ Q))(4)
(5) (P ∨ Q) → R ⊢ (P → R) & (Q → R)(5)
(6) ⊢ (P ∨ Q) → (Q ∨ P)(6)
(7) ∼(P & ∼ Q) ⊢ P → Q
(8) (P ∨ Q) ↔ P ⊢ Q → P
(9) P ↔ Q, Q ↔ R ⊢ P ↔ R
(10) ⊢ (P → Q) → (∼ Q → ∼ P)
Click here to see answer by CPhill(1987) |
Question 1208960: Use the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof.
Premise:
1.(x) [Ax ⊃ (Bx ≡ Cx)]
2.An • Am
3.Cn • ~Cm
Conclusion:
Bn • ~Bm
Click here to see answer by textot(100) |
Question 1208963: Use the quantifier negation rule together with the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof.
Premise:
1.(∃x) Ax ⊃ ~(∃x) (Bx • Ax)
2.~(x) Bx ⊃ ~(∃x) (Ex • ~Bx)
3.An
Conclusion:
~(x) Ex
Click here to see answer by textot(100) |
Question 1207201: Please use the 18 rules of natural deduction, the 4 instantiation and generalization rules to derive the conclusions of this problem. This problem MUST be done in 7 steps, as was instructed to me!
1. (x)(Bx ⊃ Cx)
2. (∃x)(Ax • Bx) /(∃x)(Ax • Cx)
Click here to see answer by ElectricPavlov(122) |
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