Tutors Answer Your Questions about Proofs (FREE)
Question 390781: Hello, i was just wondering if there were actually tutors on here that could help me with my logic class...i have been striking out everywhere i look. I am having problems with proofs and figuring out how to do them in deductive logic. thank you.
Click here to see answer by solver91311(24713)   |
Question 403583: This is my question:
Suppose that G is a group and g,h are elements of G. There exists a k in G such that kgk=h if and only if gh=m^2 for some m in G.
I have already have:
Let k be in G and kgk=h. We can perform the operation on each side of the equation to get gkgk=gh=(gk)^2. m=gk and by the closure component of a group we know that gk is in G so we know that m is in G also.
I do not get how to prove it the other way. Please can you help.
Click here to see answer by robertb(5830)  |
Question 411727: Here is a proof that I have been unable to solve. I can solve it using Indirect Proof but it is listed under the section that states it is solvable by use of the 18 rules of Implication and equivalence. It is driving me nuts!
Here it is:
1. (O horseshoe R) horseshoe S
2. (P horseshoe R) horseshoe ~S /~R
I know I can derive ~R by Hypothetical Syllogism if I could somehow get rid of the O and the P. I can use exportation to get (O dot R) horseshoe S, and (P dot R)horseshoe ~S, but I can't disconnect those statements from the ones I need to derive a tautology through Material Implication, that is:
(R horseshoe S)
(R horseshoe ~S)
So I'm stuck. This is not an assigned problem; it's one I found. I'm a pretty good beginning logic student and enjoy working all the problems I can find, but this one has me stymied!
Click here to see answer by richard1234(7193)  |
Question 437283: 3) If the account in Genesis is literally true, then the sun was not created until the fourth day. And if the sun was not created until the fourth day, it could not have been the cause of the alternation of day and night for the first three days. But either the word “day” is used in scripture in a different sense from that in which it is commonly accepted now or else the sun must have been the cause of the alternation of day and night for the first three days. Hence it follows that either the account in Genesis is not literally true or else the word “day” is used in scripture in a different sense from that which it is commonly accepted now. (G, C, A, D)
I've gotten this far -
1) G - C Premise
2) - C - A Premise
3) D v A Premise / -G v - D
4) G - A 1,2 HS
5)
Click here to see answer by richard1234(7193) |
Question 440717: Imagine a checkers tournament between Person A and Person B (A and B). They play at most 2n matches and whoever first wins n+1 matches wins the tournament (the tournament ends once one person wins n+1 matches). Two tournaments are different if they have a different sequence of games where A wins and where B wins. Assume that A wins the tournament (so the tournament has n+1 wins for A). How many different tournaments are there where B wins exactly r games (r is less than n)?
Click here to see answer by richard1234(7193) |
Question 483036: Use the 17 rules of inference to prove the arguments valid:
I did not have the right keys for some of the logical operators, so here is what they are:
~ negation
. conjunction
v disjunction
> implication
= equivalence
Thanks!!
1) 1. (S v Q) / ~P > ~S
Click here to see answer by solver91311(24713) |
Question 495926: 1)Suppose the hard disk above has 1024 cylinders, 8 tracks per cylinder, 32 sectors per track and 512 Bytes per sector. The maximum seek time is 450 msec, the time to move between adjacent cylinders is 10 msec, the rotation time is 14ms.
a) 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?
b) Find the total capacity of the disk?
c) Find the maximum access time (worst case) for 800KB of data not stored on consecutive tracks.
2)Assume that a 2400 foot magnetic tape has recording density of 6400 Bpi. Data (logical) records are 100 bytes, and the memory buffer is 10,000 bytes. What is the largest IRG that will allow 80 percent of the tape to be data?
Click here to see answer by s11042581(1) |
Question 507684: Conjecture: Find all positive integers 'a' such that there exists an integer 'm' with the property that a|(m^2+1) and a|((m+1)^2 +1).
Hint: First show that 'a' must also divide 2m+1.
I know that when m divides n it can be defined as n=(m)(q). So in this case it would be (m^2+1)=(a)(q), and so forth with the other problems. I'm not sure if this is correct but since (m^2+1)=(a)(q) and ((m+1)^2 +1)=(a)(q) so I set
(m^2+1)=((m+1)^2 +1). I then foiled, moved everything to one side and simplified and got 2m+1 with is relevant to the hint, I think. I don't know if I'm going in the right direction but I've seem to have hit a wall. Also, I don't really know how to show that a|2m+1. Please help. Thanks.
Click here to see answer by richard1234(7193) |
Question 509899: URGENT:
P. R->~Q. P->Q therefore ~R
I need to write out a proof for the following problem using repetition, motus ponen, motus tollens, double negation, etc. This is not graded, but I'm trying to understand it and any help would be appreciated.
Click here to see answer by Edwin McCravy(20055)  |
Question 516605: There exists an integer 'a' such that if a|2m+1 and/or a|(m^2+1) and/or a|(m+1)^2+1, then a|4n+7.
Note: Anywhere from 1 - 3 of the assumptions can be used to prove 'a' divides 4n+7, so you can use a|2m+1 to prove a|4n+7, or you can use a|2m+1 and a|(m^2+1)to prove a|4n+7, or you can use a|2m+1, a|(m^2+1), and a|((m+1)^2+1) to prove a|4n+7, or any other combination.
Click here to see answer by richard1234(7193) |
Question 517510: Proposition: If 'a' is a type 1 unteger and 'b' is a type 2 integer, then (a^2-b) is a type 2 integer.
Note:a type 1 integer is defined as x=3y+1 and i type two integer is defined as x=3y+2
This is what have so far:
Proof: We let a be a type 1 integer and b be a type 2 integer. We will show that a^2-b is a type 2 integer. By the definitions of a type 1 integer and type 2 integer, there are integers m and n such that a=3m+1 and b=3n+2. By substitution and the use of algebra we see that a^2-b = (3m+1)2-(3n+2)
= (9m2+6m+1-3n-2)
= (9m2+6m-3n)-1-2
= 3(3m2+2m-n)-1
I know that 3(3m2+2m-n)-1 is a type two integer, I just don't know how to re-write it so it satisfies the definition of a type 2 integer, meaning I don't know how to get it into the x=3y+2 format.
Click here to see answer by richard1234(7193) |
Question 519617: Hello,
I have a quick question and would like to see the answer thank you. Please response back as soon as possible.
The difference of the squares of two positive integers which differ by 2 is a perfect square n^2 . Find all possible values of n.
I will be waiting for your response and thank you.
Click here to see answer by Edwin McCravy(20055) |
Question 519617: Hello,
I have a quick question and would like to see the answer thank you. Please response back as soon as possible.
The difference of the squares of two positive integers which differ by 2 is a perfect square n^2 . Find all possible values of n.
I will be waiting for your response and thank you.
Click here to see answer by Mohammad123(2) |
Question 524132: There is a famous theorem in Euclidean geometry that states that the sum of the interior angles of a triangle is 180 degrees.
a)Use the theorem about triangles to determine the sum of the angles of a convex quadrilateral. Hint: Draw a convex quadrilateral and draw a diagonal.
b) Use the result in Part(1) to determine the sum of the angles of a convex pentagon.
c) Use the result in Part(2) to determine the sum of the angles of a convex hexagon.
d)Let 'n' be a natural number with 'n'> or = to 3. Make a conjecture about the sum of the angles of a convex polygon with 'n' sides and use mathematical induction to prove your conjecture.
** I've figured out a, b, and c. I've also created a conjecture for d. Here's what I have: "Let 'n' be a natural number with 'n'> or = to 3. For any convex polygon with 'n' sides, the sum of the angle of the polygon is 180(n-2)". I have my basis class which is when n=3 then the sum = 180 degrees, but I don't know how to prove my induction step. I know (k+1) must be substitued in for 'n' at some point but not sure when and what to do. Please help.
Click here to see answer by stanbon(75887) |
|
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
|
