Questions on Logic: Proofs answered by real tutors!

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Question 1150010: Is (p v q) → (~q → p) a tautology?
Click here to see answer by jim_thompson5910(35256)

Question 1150092: 1. [A v (K & J)] > (~E &~F)
2. M > [A & (P v R)]
3. M & U /~E & A
How do I continue?
Click here to see answer by jim_thompson5910(35256)

Question 1150113: I need help constructing an indirect proof using reductio ad absurdum for:
~S → (F → L), F → (L → P), therefore, ~S → (F → P)
Can the proof be performed more efficiently by using different equivalence rules?

Click here to see answer by Edwin McCravy(20054)

Question 1150289: Use natural deduction to derive the conclusion in each problem.

Use conditional proof or indirect proof as needed:

1.
F ⊃ (J ∨ ∼F)

2.
J ⊃ (L ∨ ∼J) / F ⊃ L
Click here to see answer by jim_thompson5910(35256)

Question 1150892: Prove by induction
n*1 + (n-1)*2 + (n-2)*3 + ... + 3*(n-2) + 2*(n-1) + 1*n = n(n+1)(n+2)/6
Click here to see answer by ikleyn(52777)

Question 1151203: if bill is 3 inches taller than jim and jack is 2 inches taller than jim how much shorter is jim than bill?
Click here to see answer by Boreal(15235)

Question 1153437: 11. R & (R→ S), P & (P→ T)├ S & T
Here is what I have so far
1.R&(R->S) ASSUMPTION
2. P&(P->T) ASSUMPTION

CONCLUSION- S&T
Click here to see answer by MathLover1(20849)

Question 1153481: (K->L)&(K->M)├ K->(L&M)
Click here to see answer by Edwin McCravy(20054)

Question 1154187: Solve the following proof:

1. A⊃B
2. B⊃~A
3. (AvD)vE
4. (DvE)->F / F
Click here to see answer by Edwin McCravy(20054)

Question 1154594: Solve the following Proof:
1. G => (S&T)
2. (S v T) => J
3. G /J
Click here to see answer by math_helper(2461)

Question 1155133: Use an ordinary proof (not conditional or indirect proof):

1. K∨(S • N)
2. ∼(K •∼Q)
3. ∼(N •∼Q) / Q

Click here to see answer by Edwin McCravy(20054)

Question 1155133: Use an ordinary proof (not conditional or indirect proof):

1. K∨(S • N)
2. ∼(K •∼Q)
3. ∼(N •∼Q) / Q

Click here to see answer by jim_thompson5910(35256)

Question 1155448: Prove: E ⊃ M
Click here to see answer by ikleyn(52777)

Question 1155652: SOLVE THE PROOF
P v Q, P → (T → S), P → T, S ↔ Q ├ S
1. P v Q ASSUMPTION
2. P → (T → S) ASSUMPTION
3. P → T ASSUMPTION
4. S ↔ Q ASSUMPTION

CONCLUSION- S

Click here to see answer by Edwin McCravy(20054)

Question 1156052: Logical Proofs (Solve and Show Work)
1. G ⊃ (H ⊃ K)
2. (H v ~M) ⊃ ~K
3. H / ~G
Click here to see answer by Edwin McCravy(20054)

Question 1156254: 1. (A v B) ⊃ T
2. Z ⊃ (A v B)
3. T ⊃ W
4. ~ W /∴~Z

Click here to see answer by Edwin McCravy(20054)

Question 1156256: 1. (A v B) ⊃ (C v D)
2. C ⊃ E
3. A • E /∴ E v D
Click here to see answer by Edwin McCravy(20054)

Question 1156932: Use natural deduction to derive the conclusion in each problem.

Use an ordinary proof (not conditional or indirect proof):

1. (O ⊃ C) • (∼S ⊃ ∼D)
2. (E ⊃ D) • (∼E ⊃ ∼C) / O ⊃ S
Click here to see answer by Edwin McCravy(20054)

Question 1157554: How do you work through this problem?
Use indirect proof:
1. ∼A ⊃ (B • C)
2. D ⊃ ∼C / D ⊃ A

Click here to see answer by Edwin McCravy(20054)

Question 1157735: What is the ordinary proof to solve the following argument?
P ⊃ ~M
C ⊃ M
~L v C
(~P ⊃ ~E) • (~E ⊃ ~C)
P v ~P /~L

Click here to see answer by Edwin McCravy(20054)

Question 1157890: I.Use an ordinary proof (not conditional or indirect) to solve the following arguments.
~N ⊃ (~R ⊃ C)
R ⊃ N
~C /N

Thank you!
Click here to see answer by Edwin McCravy(20054)

Question 1157893: Use Indirect Proof to solve the following argument
(E v F) ⊃ (C • D)
(D v G) ⊃ H
E v G /H
Thank you!

Click here to see answer by jim_thompson5910(35256)

Question 1157893: Use Indirect Proof to solve the following argument
(E v F) ⊃ (C • D)
(D v G) ⊃ H
E v G /H
Thank you!

Click here to see answer by Edwin McCravy(20054)

Question 1157892: II. Use Conditional Proof to solve the following arguments
J ⊃ (K ⊃ L)
J ⊃ (M ⊃ L)
~L / J ⊃ ~(K v M)
Thank you!

Click here to see answer by Edwin McCravy(20054)

Question 1157891: III. Use Indirect Proof to solve the following arguments
(K v L) ⊃ (M • N)
(N v O) ⊃ (P • ~K) / ~K
Thank you!
Click here to see answer by jim_thompson5910(35256)

Question 1157678: 1. A -> (B • C)
2. ~[(B • D) • C]
3. D

Click here to see answer by Edwin McCravy(20054)

Question 1157678: 1. A -> (B • C)
2. ~[(B • D) • C]
3. D

Click here to see answer by jim_thompson5910(35256)

Question 1157556: Use the first eight implication rules to create a proof of the following argument.
1. B v C
2. (C ⊃ D) • (D ⊃ F)
3. (B ⊃ G) • (P ⊃ H) /G v D
Click here to see answer by Edwin McCravy(20054)

Question 1157960: Use Conditional Proof to solve the following argument
E ⊃ (F ⊃ G)
H ⊃ (G ⊃ I)
(F ⊃ I) ⊃ (J v ~H) / (E•H) ⊃ J

Click here to see answer by AnlytcPhil(1806)

Question 1158177: 1. (p ⊃ z) • (z ⊃ x)
2. (p ⊃ x) ⊃ ~s
3. n v s : . n
Click here to see answer by Edwin McCravy(20054)

Question 1158611: solve the proof
~F > ~G, P > ~Q, ~F v P, (~G v ~Q) > (L • M), therefore, L
Click here to see answer by Edwin McCravy(20054)

Question 1158771: Pattern Problem
Determine the next number in the sequence 0, 10, 24, 56, 112, 190, ...
Click here to see answer by math_helper(2461)

Question 1158861: Pattern Problem
One cut of a stick of licorice produces two pieces. Two cuts produce three pieces. Three cuts
produce four pieces.
a. How many pieces are produced by five cuts and by six cuts?
Click here to see answer by ikleyn(52777)

Question 1159126: D ⊃ (F • S) / (B ⊃ D) ⊃ (B ⊃ S)
I want to use a conditional proof to prove this answer using the given premise. I don't know where to start. Should I assume D?
Click here to see answer by Edwin McCravy(20054)

Question 1160845: the absolute value of (XY) = abs(X).abs(Y)
Click here to see answer by MathLover1(20849)

Question 1161659: Suppose the hard disk above has 1024 cylinders, 8 tracks per cylinder, 32 sectors per track and 1024 Bytes per sector. The maximum seek time is 450 msec, the time to move between adjacent cylinders is 10 msec, the rotation time is 14. If the entire disk was full of data stored consecutively, how much time would it take to read the entire disk if the read/write head is already positioned on the first sector of the first track of the first cylinder of the disk?
Click here to see answer by ikleyn(52777)

Question 1162803: Please help me solve this :
o⊃(p⊃q)
P⊃(Q⊃R)
por tanto O⊃(P⊃R)
Click here to see answer by solver91311(24713)

Question 1162984: Is the following argument valid? Provide a proof for your answer.
p =⇒ (q ∧ r)
∼q
− − − − − − − − − −
∼p
Click here to see answer by jim_thompson5910(35256)

Question 1167143: Solve:
F/(G -> H) v (~G -> J)
Click here to see answer by solver91311(24713)

Question 1167228: Prove or disprove that h(x)=2x^3+1, where in h: integers (Z) → integers (Z) is a bijective function.
Click here to see answer by ikleyn(52777)

Question 1167696: Setting up a prove in Fitch notation
Premises:
PvQ
~QvR

Conclusion; PvR
Click here to see answer by solver91311(24713)

Question 1168996: Given: A->~B
~(C^~A)
B
~C-> D
Prove:D
Click here to see answer by Solver92311(821)

Question 1169463: Prove ¬F =⇒ G, F =⇒ H ∴ G ∨ H
Click here to see answer by math_helper(2461)

Question 1169573: Use an ordinary proof (not conditional or indirect proof):

1. ∼N ⊃ (∼R ⊃ C)
2. R ⊃ N
3. ∼C / N
Click here to see answer by math_tutor2020(3816)

Question 1169574: Use conditional proof:

1. G ⊃ (E ⊃ N)
2. H ⊃ (∼N ⊃ E) / G ⊃ (H ⊃ N)
Click here to see answer by math_tutor2020(3816)

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