Questions on Logic: Proofs answered by real tutors!

Tutors Answer Your Questions about Proofs (FREE)

Question 1207678: Use natural deduction to derive the conclusion in each problem.
Use an ordinary proof (not conditional or indirect proof):

1.E ⊃ (S ⊃ T)
2.(∼L • M) ⊃ (S • E)
3.∼(T ∨ L) / ∼M
Click here to see answer by Edwin McCravy(20054)

Question 1207830: Construct a formal proof of validity for the following arguments by means of Natural Deduction. You are NOT allowed to use Conditional Proof or Indirect Proof
(1)
1. (A ⊃ B) • (C ⊃ D) // (A • C) ⊃ (B • D)
Click here to see answer by mccravyedwin(406)

Question 1208642: Prove this
1. F∨~I
2. I∨H
3. ~(G↔J)→~H ∴ [(~G∨~J)∙(G∨J)]→F
Click here to see answer by math_tutor2020(3816)

Question 1208734: Create a proof for the following argument.
1.~D
2.B ⊃ (C ⊃ D) /~(B • C)
Click here to see answer by math_tutor2020(3816)

Question 1208772: 1. (K ¡ L) ⊃ (M ● N) 2. (N ¡ O) ⊃ (P ● ∼K)/ ∼K

Click here to see answer by Edwin McCravy(20054)

Question 1208773: Premise:
1.
(L ≡ N) ⊃ C
2.
(L ≡ N) ∨ (P ⊃ ~E)
3.
~E ⊃ C
4.
~C
Conclusion:
~P

I need the proof but im struggling
Click here to see answer by math_tutor2020(3816)

Question 1208888: 1. (E→~K)
2. (M∨(~K.~H))
3. (~M∨E) .: ~K
Construct a proof to show that the following argument is valid. You can use any proof technique you like, but you may find indirect proof helpful.

Click here to see answer by Edwin McCravy(20054)

Question 1208837: Add the missing rule citations for these proofs:
1.(F → (G → ¬H))PR
2.((F ∧ ¬W) → (G ∨ T))PR
3.(F ∧ ¬T)PR
4.(W → T)PR
5.F
6.¬T
7.(G → ¬H)
8.W
9.T
10.⊥
11.¬W
12.(F ∧ ¬W)
13.(G ∨ T)
14.G
15.¬H
17.T
18.⊥
19.¬H
20.¬H
Click here to see answer by ikleyn(52776)

Question 1208943: prove the argument is valid using the method of natural deduction:
1. (~N wedge R) horseshoe B
2. A wedge ~(M horseshoe N) / therefore A horsehoe B
Click here to see answer by math_tutor2020(3816)

Question 1208944: Prove that the argument is valid using the method of natural deduction.
tilde (Q horseshoe tilde R)
tilde (tilde P dot Q) / therefore tilde R horseshoe (P dot Q)
Click here to see answer by math_tutor2020(3816)

Question 1209011: 1. W ⊃ Z
2. W v Z / ∴ Z
Click here to see answer by mccravyedwin(406)

Question 1209011: 1. W ⊃ Z
2. W v Z / ∴ Z
Click here to see answer by math_tutor2020(3816)

Question 1209090: Premise:
1.
~S
Conclusion:
~(F • S)
What is proof, line and rule?
Click here to see answer by math_tutor2020(3816)

Question 1209177: Premise:
H & ( C & T )
~ ( ~ F & T )
Conclusion:
F

Click here to see answer by math_tutor2020(3816)

Question 1206907: 1. H > (M > E)
2. ~[(M > H) > E]
3. (I + O) > [M + (X = P)]
4. [(K v B) > ~M] > (~I v ~Z)
5. [I > ~(Z v O)] > (A > ~K)
6. E v (K v A) / A = ~K
Click here to see answer by CPhill(1959)

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)

Question 1207200: Please use the 18 rules of natural deduction, the 4 instantiation and generalization rules to derive the conclusions of this problem.
1. (x)(Bx ⊃ Cx)
2. (∃x)(Ax • Bx) /(∃x)(Ax • Cx)
Click here to see answer by ElectricPavlov(122)

Question 1209282: 1. (~(~Z v H) ⊃ ~T)
2. ((S ⊃ Z) ⊃ ~H)
∴ (Z ⊃ ~T)

what's the next steps for this?

Click here to see answer by AnlytcPhil(1806)

Question 1209282: 1. (~(~Z v H) ⊃ ~T)
2. ((S ⊃ Z) ⊃ ~H)
∴ (Z ⊃ ~T)

what's the next steps for this?

Click here to see answer by math_tutor2020(3816)

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 1208962: Premise:
1.(∃x) (Ax • Bx) ∨ (∃x) (Cx ∨ Dx)
2.(∃x) (Ax ∨ Cx) ⊃ (x) Ex
3.~Em
Conclusion:
(∃x) Dx
Click here to see answer by textot(100)

Question 1208961: Premise:
1.(∃x) (Ax • Bx) ⊃ (x) (Cx • Dx)
2.(∃x) Ax ⊃ (x) (Bx • Cx)
3.Ae
Conclusion:
(∃x) (Dx • Bx)
Click here to see answer by textot(100)

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 1208947: Prove that the argument is true using the method of natural deduction. You may use cp or ip.
1. (N wedge R) horseshoe B
2. A wedge tilde(M wedge N) / therefore A horseshoe B
Click here to see answer by textot(100)

Question 1208946: Prove that the argument is valid using the method of natural deduction.
1. Q
2. (R horseshoe Q) horseshoe (P dot tilde P) // S
Click here to see answer by textot(100)

Question 1208945: Prove that the argument is valid using the method of natural deduction.
1. tilde(S dot tilde R)
2. tilde (P tribar S)
3. R wedge V / therefore tilde R horseshoe (P dot Q)
Click here to see answer by textot(100)

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(1959)

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(1959)

Question 1188876: Use the finite universe method to prove that the following argument is invalid:

1. (x)Ax⊃(∃x)Bx
2. (∃x)Ax / (∃x)Bx
Click here to see answer by CPhill(1959)

Question 1209588: ((A & B) & C) & D, (D & C) → F, (B & C) → G, (A & D) → H ├ H & (G & F)

Click here to see answer by Edwin McCravy(20054)

Question 1181635: Find the truth value of the following: Show the solution.
4. (q∨r)↔[(¬q→(r∧¬p))]
5. (¬s↔(r→¬q))↔[(s∨p)∧¬(q∧r)]
Click here to see answer by CPhill(1959)

Question 1181634: Find the truth value of the following: Show the solution.

3. [(q∨¬p)↔(r→p)]→(q∨s)

Click here to see answer by CPhill(1959)

Question 1181633: Find the truth value of the following: Show the solution.

2. ¬(r→s)∨[(p∧¬q)∨¬s]

Click here to see answer by CPhill(1959)

Question 1181632: Find the truth value of the following: Show the solution.
1. (p∨r)→[(q↔s)∧p]

Click here to see answer by CPhill(1959)

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(1959)

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(1959)

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)
---------------------
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(1959)

Question 1178948: 1. (G • H) v (M • G)
2. G ⊃ (T • A) /A

Click here to see answer by CPhill(1959)

Question 1178947: 1. ~(U v R)
2. (~R v N) ⊃ (P • H)
3. Q ⊃ ~H /~Q

Click here to see answer by CPhill(1959)

Question 1178946: 1. ~(K v F)
2. ~F ⊃ (K v C)
3. (G v C) ⊃ ~H /~(K v H)

Click here to see answer by CPhill(1959)

Question 1176997: ~F → G I - F v G

Click here to see answer by CPhill(1959)

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(1959)

Question 1171515: Hey, I hope you are doing well. I have these homework questions that I can't figure out.
A, ¬F → ¬A ⊢ D → (¬E → F)
I'm supposed to construct a formal proof
Thank you!
Click here to see answer by CPhill(1959)

Question 1171460: Can you help me prove O ⊃ S only using the first 18 rules?
O ⊃ (Q • N)
(N v E) ⊃ S.../ O ⊃ S
Click here to see answer by Edwin McCravy(20054)

Question 1171459: Can you help me prove for F only using the first 18 rules?
I v (N • F)
I ⊃ F..../F
Click here to see answer by CPhill(1959)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485