Questions on Logic: Proofs answered by real tutors!

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Question 760899: Complete the following proofs using the Conditional Proof method.
1) 1. ~(P ∙ ~Q)
2. ~P → ~R
3. (R ∙ Q) → S / R → S
______________________

2) 1. (P ∙ Q) v (R ∙ S)
2. R → L / ~P → L
____________________

Complete the following proofs using the Indirect Proof method.
3) 1. A → B
2. A → C
3. ~B v ~C / ~A
_______________

4) 1. M v (O ∙ ~N)
2. ~M v ~N / ~N
______________

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Question 761162: Can you prove/show that the following is a tautology, without using a truth table: [(p v q) ^ (p -> r) ^ (q -> r)] -> r
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Question 762545: State which of the following are logical statements and then classify the statements as true or false.
a) 1 + 4 = 6
b) She is in our class
c) Butte is the capital of Montana
d) 3 + x = x + 3

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Question 766444: I can only use the rules of inference/replacement
1) R v ~T
2) ~T -> O
3) ~O
∴ R
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Question 766586: please help me solve this problem "you have 2 bucket. One is of 3 litres and another one is of 5 litres. There is no mark on them. How will you measure 4 litres using them? "
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Question 767587: 12 men can build a wall in 4 days.how many days will 3 men take to build the same wall?

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Question 769172: please help me solve this question: show that 4 does not divide (n^2+2) for any n
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Question 769399: If 5 ppls takes 10 days to build a wall then 15 ppls take how many days to build the same wall

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Question 770841: INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. H v (~T > R) 2. Hv (E > F) 3. ~T v E 4. ~H & D / R v F
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Question 774764: M = y/x -b/x
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Question 782764: The sum of 4 even numbers is divisible by 4. Is this statement, Always true?, Sometimes true?, or Never true? And why?
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Question 791503: Given:
if R, then T
R and M
if T, then k
Prove:
k
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Question 792747: Show that A = B, when A = {a | a is even number} and B = {b| b is multiple of 2}.
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Question 796725: 1.prove that the square root of 5 is an irrational number?

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Question 796919: Prove the argument:
A->D
D->E
A or B
B->C
~C
Therefore, C
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Question 797896: Hi! My goal is to show that the members of the pair of sentences are equivalent in SD.
The sentences are A & (B&C) and (A&B) & C.
I know I start off by deriving A & (B&C) using the assumption (A&B) & C, but I'm not sure what to do next.
Click here to see answer by ayomide(2)

Question 798503: This question relates to finding partial derivatives.
Burger's Equation is a partial differential equation, used for describing wave processes in acoustics and hydrodynamics,
(let d= partial derivative, a=alpha, and L=lambda)

verify that

is a solution, where L and a are arbitary constants
thank-you for any help
Click here to see answer by KMST(5328)

Question 799059: Please help me prove this!
(A&B)->~A therefore ~B
Click here to see answer by Edwin McCravy(20054)

Question 799484: H > K
C = D
~C > ~K
Therefore H > D
What are the steps involved in determining this conclusion? I really need to know if I did this correctly.
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Question 802791: Construct a formal proof in fitch format for the following:
1. Premise: A->B
Conclusion: A->(BvC)
2. No premise
Conclusion: P->(Q->P)
3.Premise: P<->~P
Conclusion: ⊥
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Question 804680: Prove that for all positive integers n,
1�1!+2�2!+3�3!+...+n�n!=(n+1)!-1
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Question 805449: could you put un- with wind
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Question 805588: use the product rule and the chain rule to derive the quotient rule? thanks a lot!!! i really appreciate your help. thank you :)

Click here to see answer by Edwin McCravy(20054)

Question 806075: 1. X or Y Premise
2. ~X Premise
3. ?
Click here to see answer by jim_thompson5910(35256)

Question 806601: hai....my frnd asks me this question, it is prove that 15-6=10...pls solve this ques and tell me the logic?????
Click here to see answer by richwmiller(17219)

Question 807023: Prove that 2 + sqrt 27 is not rational. really stuck please help me.
Click here to see answer by sheldonbbtrocks(115)

Question 807638: proof by contradiction if 3n+1 is odd then n is also odd
Click here to see answer by fcabanski(1391)

Question 808290: whether (~p disjunction (p-->q))-->~q is a tautology without using truth table?

Click here to see answer by Edwin McCravy(20054)

Question 808526: Write a paragraph proof/or two column proof:
NEED HELP ASAP! PLEASE!
Click here to see answer by richwmiller(17219)

Question 808810: do a proof for the following arguments:
1. XvY
2. ~F
3. D > X
4. ~Y&F /~D&F (conclusion)

1.x > ~D
2. XvC
3. C>F
4. KvP
5. ~D>B / (BvF)vD (conclusion)

>= horshoe
v= wedge
~tilde
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Question 811816: Use Fitch to give a proof of this arguments validity
~ExCube(x)
--
Ax~Cube(x)
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Question 812994: I'm currently working on fractions,trying to change improper fractions to whole or mixed numbers. I come across the problem 15/9 and its telling me 9 goes in 15 twice how is that possible when 9 plus 9 is 18. Please help I am seriously confused!!!!
Click here to see answer by jim_thompson5910(35256)

Question 816261: why sin theta is equal to tan theta when angle is minimum
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Question 816261: why sin theta is equal to tan theta when angle is minimum
Click here to see answer by Edwin McCravy(20054)

Question 824313: how to proof the arguments:
1. T ⊃ G
2. S ⊃ G
∴ (T ∨ S) ⊃ G
Click here to see answer by Edwin McCravy(20054)

Question 824552: How to disprove that if a < b then a^2 < b^2. So, you have to find a set of values that would disprove the inequality.
Click here to see answer by tommyt3rd(5050)

Question 835126: Prove that if a set is an improper subset of another set, then the two set are equal
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Question 836405: two planets are in orbit around the sun. both move in a clockwise direction. the outer planet takes 22 years to complete an orbit while the inner planet takes 10 years.when will they next both be in their current positions again?
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Question 836543: PQR, QP, Q solve for R
Click here to see answer by Edwin McCravy(20054)

Question 839172: Let W be a subset of R3 be the subspace spanned by the vectors w1 and w2 below. Find the coordinates of w with respect to the basis {w1, w2} (In particular, your answer will show that w is an element of W)
w1=(2, -1, 4)
w2=(5,2,-3)
w=(-6, -15, 40)
Click here to see answer by Fombitz(32388)

Question 839173: Let S be the set of all solutions to the differential equation y^n = -y. THe functions y = sinx and y = cosx are solutions and are linearly independent (becasue if asinx+bcosx=0 all x then a=b=0). In fact, one can show that B = {sinx, cosx} is a basis of S.
(a) Show that y = sin(x+(pi/3)) is an element of S.
(b) Find the coordinate vector [sin(x+(pi/3)]B Hint: use a trig sum formula
Click here to see answer by richard1234(7193)

Question 840954: what is the difference between ⊨ and ⊢ ?
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Question 847372: Connet all the vertices with 2 colours, such that there exists no triangle with all 3 sides of the same colour. (Triangles not connected by vertices on each point do not count) If this is impossible, please explain, or prove why.
The vertices are arranged as such:
⠀�⠀⠀�
�⠀⠀⠀⠀�
⠀�⠀⠀�
Each line should connect to every vertice to each other. There should be 20 triangles.
Click here to see answer by richard1234(7193)

Question 847697: Prove or disporove. If (n^3)+2 is odd then n^2 is odd where n is an element of all integers.
Click here to see answer by jim_thompson5910(35256)

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