Questions on Logic: Proofs answered by real tutors!

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Question 607203: Can you please help me solve the following proof?
1.D>(A*G)
2.(AvB)> [(C>Q)*D] // A (triple bar)D
> equals wedge
* equals dot

Click here to see answer by jim_thompson5910(35256) About Me 

Question 607205: I have started the following proof but am not sure how to finish. thanks!
1. G>(H>K)
2. (Hv~M) > ~K
3. H // ~G
4. ~Gv(H>K)
>equals horseshoe

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Question 607354: ~(A=B)
A /~B

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Question 607705: 1. S v (U*P)
2. (SvU)>R // R
> equals horseshoe

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Question 607845: This may seem easy, but I don't get how to find the answer to this
1. F <-> G
with the final answer of -F <-> -G

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Question 608105: 1. p>q
2. ~q /~p
3.??????
How do I get to the conclusion? I'm new at this and don't really understand it yet. I thought line 3 looked like this: 3. ~p 1,2, MT

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Question 608113: 1. pV(q . r)
2. ~p /q . r
How do I get q . r? Thought line 3 was: (pVq) . (pVr) 1, Dist......Now I'm stuck and don't know how to get q . r Please help!

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Question 608115: 1. ~pVq
2. p /q
3.?????
I figured line 3 is: ~p . ~q 1,DM ?? Then line 4: q 2,3 DS....Probably way off. Help is much appreciated!

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Question 607887: Determine by showing work and using any method whether argument is valid
The number 91 is prime just in case it is not composite. The number 91 is not both prime and divisible by 2. The number 91 is divisible by 2. Therefore the number 91 is composite.

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Question 608410: Can you prove this identity:
sin%283x%29%2Fsin%28x%29 - cos%283x%29%2Fcos%28x%29 = 2

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Question 610046: my question is that i got the same conclusion as my instructor but with different methods and i was wondering if that is still ok. the instructions are to add just 2 statements to the premises to produce a formal proof of validity. ill provide my answers and his, thanks a lot.
1. (S.T) v (U.V)
2. ~S v ~T
Therefore U.V
My answer
3. (U.V) v (S.t) 1, Com.
4. U.V 3, Taut.
his answer
3. ~(S.T) 2, Dem.
4. U.V 1,3 D.S.




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Question 613312: Write a formal proof of validity for the given arguments
A)
1. (R>S)
2. V v~S
3. ~V/.'.~R
B)
1. W.(XvY)
2. W
3. ~X/.'.YvZ
C)
1. A * ~ B / .'. B > C

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Question 615204: What is the answer to this proof: 1.(E.V) v(M.U)2.~E conclusion /M
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Question 616027: Hi just needed some help in solving this equation it may be invalid so means that it can't be solved or it may be valid meaning it can be solved and I am stuck so not sure if I am right or not. Here it is:
VxEy(Rxy) l- VxEy(Rxy & Ez(Ryz))
Thanks

Click here to see answer by Alan3354(69443) About Me 

Question 616557: 1. D
2. ~C
3. (A v B) -> C
4. [(~A • D) • ~B] -> (P -> Q) :. ~P v Q

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Question 617771: 1. R v ~T
2. ~T>O
3. ~O
:. R

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Question 617774: 1. B > (C . D )
2. R
3. B
:. (C . D ) . R

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Question 617772: 1. (W . (R v T ) ) > P
2. ( P v L ) > ~ H
3. W
4. R
:. ~ H

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Question 618022: Use induction to prove that 1*2+2*3+3*4+...+n(n+1)=(n(n+1)(n+2))/3
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Question 619631: What symmetry of the letter A?
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Question 622920: The head of a fish is 9 inches long. The body length of the fish between the head and the tail is equal to the head plus the tail. The tail length is equal to the head plus one half of the body length between the head and the tail. This is enough information to work out that the total length of the fish is what? (Pencil and paper may be used.)
Click here to see answer by KMST(5328) About Me 

Question 626898: Construct a truth table for (p V ~q) ↔ p

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Question 627286: Is it possible that two different reasons can justify a step in a proof? Why or why not? Is it easier to work down the columns or across the rows in a proof? Why? Make sure you justify your opinion.
Click here to see answer by solver91311(24713) About Me 

Question 630377: Construct a truth table for q ↔ (p^ ~q)
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Question 632553: In the same amount of time a new production assembly robot can assemble 8 times as many
transmissions as an old assembly line. If the new robot can assemble 'x' transmissions per hour, how
many transmissions can the new robot and the old assembly line produce together in five days of round
the clock production.

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Question 632981: When you square any integer, the last digit of the number you get will never be an eight.
Is this statement true, false, or sometimes true. Justify your result.
to prove this i've tried...
1^2=1 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2 = 100
as you can see this is true for single digits i've tried double digits as well up till 30^2, and clearly enough the last digit is never an eight.
from what i've got above im guessing that this statement is true!

Click here to see answer by Edwin McCravy(20054) About Me 
Question 632981: When you square any integer, the last digit of the number you get will never be an eight.
Is this statement true, false, or sometimes true. Justify your result.
to prove this i've tried...
1^2=1 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2 = 100
as you can see this is true for single digits i've tried double digits as well up till 30^2, and clearly enough the last digit is never an eight.
from what i've got above im guessing that this statement is true!

Click here to see answer by richard1234(7193) About Me 

Question 633618: I need help completing this proof.
1. R&S, S->(P->Q), Q->P |- P<->Q

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Question 636279: 28 liters oil in a pot how divide the oil in 15 liters pot and 28liters pot but each pot have 14 liters oils and also have a13liters pot, how tell me this possible
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Question 640743: please help to construct a formal proof of validity
1.p>q /.'.(q.r)>p

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Question 643819: Prove that |x + y| ≦ |x| + |y|
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Question 643963: prove that abs(x-y)>abs(x)-abs(y)
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Question 644513: Let S and T be sets. Prove that if x ∉ S ∩ T, then X ∉ S or X ∉ T.
Click here to see answer by jim_thompson5910(35256) About Me 

Question 644532: Prove or give a counterexample to each statement.
∀x ∈ ℝ, ((x^2) + 5x + 7 > 0)

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Question 644546: Prove or give a counterexample.
S ∪ T = T ⇔ S ⊆ T

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Question 647591: BOSTON IS THE CAPITAL OF MASSACHUSETTS
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Question 648551: the one by on step proof for a-(a-b)=2a-b

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Question 654642: Given: a --> c Prove: b
~a --> b
~c

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Question 659373: if x is a prime interger then x is odd
Click here to see answer by Alan3354(69443) About Me 

Question 664426: Given ¬(p∧q), prove (¬p∨¬q).
Click here to see answer by Edwin McCravy(20054) About Me 

Question 665002: What is the Formal Proof for
P v (Q ^ R)?

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Question 665955: 1. (QvR)->(WvU)
2. W->P
3. Q.T
4. U->Z
5. S->M
6. Sv~Y
7. (PvZ)->~M :. ~Y
I need help solving this.
I have the following information:
8. Q 3, Simp
9. T 3, Simp
10. Q∨R 8, Add
11. W∨U 1,10, MP
12. U∨W 11, Com
13. ~~Q 8, DN
14. ~~T 9, DN
15. ~~Q∙~~T 13,14, Conj
16. ~(~Q∨~T) 15, DeM
17. ~(~T∨~Q) 16, Com
18. P∨Z 11,2,4, CD
19. ~M 7,18, MP
20. ~S 5,19, MT
21. ~S∨~Y 20, Add
22. ~Y∨~S 21, Com
23. ~(Y∙S) 22, DeM
24. ~(S∙Y) 23, Com

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Question 668485: I am just so confused! Here's the problem.
I am supposed to derive the following problem: {(G > J) & [(~K > ~H) & (G v H]} > (J v K)

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Question 668746: 1. ~~G
2. (P•Y)v(X->~W)
3. (P•Y)->~G
4. ~W->~G
/~X

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