Questions on Logic: Proofs answered by real tutors!

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Question 990138: Given: EF is parrel to EG
D is in the interior of FEG
Click here to see answer by Timnewman(323)

Question 990654: five students-Joe,Kim,Linda,mark and nicole are enrolled in grades ranging from first to fifth.
EACH STUDENT IS IN A DIFFERENT GRADE.
MARK IS IN A LOWER GRADE THAN KIM
NICOLE AND LINDA ARE IN THE FIRST AND FIFTH GRADES ALTHOUGH NOT NECESSARILY IN THAT ORDER
Which of the following must be false?
a.Kim is in a lower grade than Nicole
b.Kim is in the second grade
c.Joe is in the second grade
d.Joe is in the third grade.
e.Kim is a higher grade than Joe
If Mark is in the third grade which of the following must be true/
A.Joe is in a higher grade than Kim.
B.Kim is in a lower grade than Nicole,
C.Nicole is in the first grade.
D.Joe is in a lower grade than Mar.
E.Linda is in the first grade.
Pls answer asap!!!!!!!!!!!!!
Click here to see answer by solver91311(24713)

Question 993881: If abs(x)=0
Then prove that x=0 using axioms
Click here to see answer by rothauserc(4718)

Question 994880: not very sure if this is in logic but I need some proof.
I need to prove that this sequence ends in
any help is very much appreciated
thanks
Click here to see answer by Edwin McCravy(20054)

Question 995351: How do I turn this statement into a conditional statement:
All cars have a dashboard.
Click here to see answer by stanbon(75887)

Question 995400: i need to prove that by mathematical induction.
thanks in advance to all.
Click here to see answer by Alan3354(69443)

Question 995573: if the sum of the digits of a 3 digit number is divisible by 9, prove that the 3 digit number is also divisible by 9
Click here to see answer by ikleyn(52775)

Question 996085: Solve the following using rules of replacement:
(E → T) ∧ (T → O), (�O ∨ E)∴ (O ↔ T)
Click here to see answer by jim_thompson5910(35256)

Question 996083: Solve the following using rules of replacement:
R ∨ V , R → (H ∧ S), V → (H ∧ N) ∴ H ∧ (S ∨ N)
Click here to see answer by jim_thompson5910(35256)

Question 996079: Replacement Rules to solve the following proof:
(�B∨ �H)→ M,K ∧ �M∴ B

Click here to see answer by jim_thompson5910(35256)

Question 996120: Solve the following using replacement rules:
�S → O, O → S ∴ S
Click here to see answer by jim_thompson5910(35256)

Question 996470: tenyears ago jane was four times as old as maria now she is only twice as old as maria.find their present age
Click here to see answer by Alan3354(69443)

Question 996797: I do not know how to start it as i only know how to solve it with a truth tree and not without one. Here is the question , i have uploaded it to imgur. http://imgur.com/gJka78m
Thanks for your help.
Click here to see answer by ikleyn(52775)

Question 996914: 1. (A->B) v (C�D)
2.A
//-B->C
Click here to see answer by jim_thompson5910(35256)

Question 998517: prove that rational+irrational=irrational
Click here to see answer by Edwin McCravy(20054)

Question 999025: Hi, I need help with finishing these proofs for my PHI class I am so confused! :(
[1]
1. ~T
2. R ⊃S
3. S⊃T Conclusion: /~R

[2]
1. (F � P)⊃~Y
2. F
3. J⊃Y
4. P Conclusion: /~J

[3]
1. A v (Bv D)
2. ~A
3. B⊃X
4. D⊃~H
5. ~X Conclusion: /~H

Click here to see answer by Edwin McCravy(20054)

Question 998980: Using the logical rules of replacement and implication, I was supposed to solve this logical proof. and am now very lost:
(Key: . being used for conjunction
+ being used for disjunction
> being used for implication)
Premise 1: W+P
Premise 2:~(W.S)
Premise 3: ~(S.P)
Conclusion~(S.U)
I have tried everything! Please help.
Click here to see answer by Edwin McCravy(20054)

Question 996678: I'm having a really hard time with the following proof:
A&B, AvC :. (A->B) & (C->A)
My prof has warned us that the second premise, AvC, is a distraction, but I don't really understand how to do this then.
Click here to see answer by Edwin McCravy(20054)

Question 1000819: 1. ~P>[~P>(Q>P)]
2. ~P / :. ~Q
Click here to see answer by Edwin McCravy(20054)

Question 1001436: Construct a direct proof of validity for the following argument.
Restriction: DO NOT USE IMPLICATION OR DISTRIBUTION > means Horseshoe
1. B >(A>C)
2. (B > C) > F /A > F

Click here to see answer by Edwin McCravy(20054)

Question 1002416: Prove that sec(-x)/csc(-x)=-tanx
Click here to see answer by fractalier(6550)

Question 1003230: S>(~U�B) / (~H>S)>(~H>B)
Using conditional proof
The horseshoe is >
Click here to see answer by jim_thompson5910(35256)

Question 1003311: I have been on these proofs for days and I can't seem to figure my homework out. Thank you for looking at this problem. Here is an example that would help me if figured out.
N>[(P>P)>W] / W>{[M>(I>M)]>(O.~O)} // ~N
The > represents the horseshoe
Thanks again.
Click here to see answer by jim_thompson5910(35256)

Question 1003832: I can't figure out this exercise
B v R / (R v D)> J / ~J>~(B v A) // J
I have to use Indirect Proof but can only figure it out using Conditional.
Click here to see answer by Edwin McCravy(20054)

Question 1003826: Example:
1. A
2. A>B / B
3. B 1,2 MP ←You add this line

1. G > H
2. ~H / ~G
3.
1. J > K
2. K > (L * M) / J > (L * M)
3.
1. O v P
2. ~O / P
3.
1. R * S / S
2.
1. R
2. T / R * T
3.
1. W / W v X
2.
1. (X > Y) * (Y > Z)
2. X v Y / Y v Z
3.
1. (C * D) > (E v F)
2. C * D / E v F
3.
1. (G > H) > (I * J)
2. ~(I * J) / ~(G > H)
3.
1. (J v K) > ~(L > M)
2. ~(L > M) > N / (J v K) > N
3.
1. O v (P v Q)
2. ~(P v Q) / O
3.
1. R * (S v T) / R
2.
1. R > S
2. S > (T v U) / (R > S) * (S > (T v U))
3.
1. W * X / (W * X) v (X * Y)
2.

Two-Step Proofs. Complete the following proofs. They can be done in two steps using the rules from 7.1 and 7.2 of your text. There may be more than one way to do some of the proofs. 14 points.
Example:
1. A
2. A > B
3. B > C / C
4. B 1,2 MP ← You add either version → 4. A > C 2,3 HS
5. C 3,4 MP of lines 4 and 5 5. C 1,4 MP

1. ~C
2. A > B
3. B > C / ~A
1. D > E
2. F > G
3. D v F / E v G
1. A * B / A v C
1. (H v I) > J
2. H / J
1. (H * I) > J
2. H
3. I / J
1. H > (I * J)
2. H / J
1. (K * L) v (M * N)
2. ~(K * L) / N

Proofs with Translation. Translate the following proofs into symbols, using the letters suggested. Each letter should stand for a simple sentence. Then do the proofs. 12 points.
Example:
If we are morally responsible for our actions, we have free will. If we are not morally responsible for our actions, jails should be emptied. We don�t have free will. Therefore, jails should be emptied. (M, F, J)
You write everything that follows:
M = We are morally responsible for our actions
F = We have free will
J = Jails should be emptied.
1. M > F
2. ~M > J
3. ~F / J
4. ~M 1,3 MT
5. J 2,4 MP

1. Either the mind is identical to the brain, or it is immaterial. If the mind is immaterial, it doesn�t make any difference. The mind makes a difference. Therefore, the mind is identical to the brain. (B, I, D)
2. If there is not an afterlife, then all is hopeless. If all is hopeless, despair is the right attitude. Despair is not the right attitude. Therefore, there is an afterlife. (A, H, D)

Click here to see answer by ikleyn(52775)

Question 1003907: Proofs
(tan x + tan y)/(cot x + cot y)
Click here to see answer by richard1234(7193)

Question 1004972: I need help deriving the conclusion (using CONDITIONAL proof). You can use all 18 rules.
1. (AvB)⊃(CvD)
2. (CvE)⊃D /A⊃D
Click here to see answer by jim_thompson5910(35256)

Question 1004998: Does this proof look correct to you? If you notice any mistakes please let me know! Thank you!
1. A⊃(B⊃C)
2. (A⊃C)⊃D / B⊃D
3. B ACP
4. A ACP
5. B⊃C 1,4, MP
6. C 3,5, MP
7. A⊃C 4-6, CP
8. D 2,7, MP
9. B⊃D 3-8, CP
Click here to see answer by jim_thompson5910(35256)

Question 1005236: F > ~G
~F > (H > ~G)
(~I v ~H) > ~~G
~I
/ ~H
Click here to see answer by jim_thompson5910(35256)

Question 1005369: I need to prove the following:
M->(K->L)
(LvN)->J
/M->(K->J)
Click here to see answer by jim_thompson5910(35256)

Question 1005719: How do I prove:
P, ~(P&Q) ⊢ ~Q

Click here to see answer by jim_thompson5910(35256)

Question 1005817: Prove that if a>b>0 then a^3>b^3
Click here to see answer by AnlytcPhil(1806)

Question 1005466: 1) 1. A -> H
2) 2. /(A&B) -> H
Click here to see answer by AnlytcPhil(1806)

Question 1005915: Construct proofs to show the following are valid:
1. ~E
2. F->(DvE)
3. ~D :. ~F

ALSO
1. Z->(U*X)
2. ~[(U*W)]
3. W :. ~Z
Click here to see answer by Edwin McCravy(20054)

Question 1005914: annotate the following proofs
1. ~~P*~P :. w
2. ~~P
3. ~~PvW
4. PvW
5. ~P
6. W
Click here to see answer by Edwin McCravy(20054)

Question 1004823: (∼∼A&C) ∴ (A∨∼∼C)
What is the proofs for this argument?
Click here to see answer by Edwin McCravy(20054)

Question 1006156: H => J
-------
:. ~J => ~H

I know to use the box and that there will be a box inside the first box which will include the negation in rule. I'm just not quite sure how they all go together.
Click here to see answer by jim_thompson5910(35256)

Question 1006581: Q∨P
R→~P
R→Q
Here is what I put but I have not been able to pass correctly. Feedback is the proof solution is wrong. Any help would be great.
Solution
1) Q∨P
2) R→~P
3) Q (SIMP 1)
4) P (SIMP 2)
5) R (MP 2, 4)
6) R→Q (HS 3, 5)
Simplifying 1, we derive lines 3 and 4. Line 5 comes about as a natural deduction of line 2 and 4. Using DS rule, we derive line 6 from line 3 and 5.

Click here to see answer by jim_thompson5910(35256)

Question 1008772: 1. (R v S) > (H & ~G)
2. (K v R) > (G v ~H) / ~R

Click here to see answer by jim_thompson5910(35256)

Question 1008806: 1. Q ⊃ (H � ∼F)
2. ∼(Q � ∼M)
3. ∼G ⊃ (Q � ∼M)
Click here to see answer by Edwin McCravy(20054)

Question 1008802: 1. N > (F & A)
2. B > (R & F) / (N v B) > (A v R)
Click here to see answer by Edwin McCravy(20054)

Question 1008769: i need help solving this indirect proof
1. (R v S) > (H & ~G)
2. (K v R) > (G v ~H) / ~R
and also help on a conditional proof
1. N > (F & A)
2. B > (R & F) / (N v B) > (A v R)

Click here to see answer by Edwin McCravy(20054)

Question 1009036: Prove the argument valid. Where = stands for a bi-conditional.
~(A & B) = ~C
(D v E) > C // E > A
Click here to see answer by jim_thompson5910(35256)

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