Tutors Answer Your Questions about Proofs (FREE)
Question 567801: Proposition 1.8
If m is an integer, then (-m)+m=0
Proof
Let m be an element of Z
There exist a (-m) in an element Z Axiom 1.4
such that m+(-m)=0
m+(-m) = (-m)+m Axiom 1.1(i)
= 0 Q.E.D
That's how I assume it is proven but it would be nice if someone could double check and make sure it is correct and also correct it. Thanks
Click here to see answer by richard1234(4789)   |
Question 563757: Can you please help me with this probability question...
A person spins the pointer and is awarded the amount indicated by the pointer.
It costs $5 to play the game. The diagram shows a circle divided into 3 parts. The pointer points to the 1/2 section marked $2. The 1/4 section is marked $20, and the other 1/4 section is marked $5.
Determine:
The expectation of a person who plays the game.
The fair price to play the game.
Click here to see answer by stanbon(48502) |
Question 562200: There is a famous theorem in Euclidean geometry that states that the sum of
the interior angles of a triangle is 180.
(a) Use the theorem about triangles to determine the sum of the angles of
a convex quadrilateral.
(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.
Click here to see answer by richard1234(4789) |
Question 551411: Given:
If schools close, then workers will lose their jobs
If we save fuel, then workers will not lose their jobs
We save fuel or there is an energy crisis
Schools will close
PROVE: There is an energy crisis
Click here to see answer by Theo(2967)  |
Question 548064: Prove that the function is bijective. The function is f: N--->Z f(x)=(1+(−1)^x * (2x − 1)) /4
I tried to attempt it using induction. I did a base case for subjectivity of f(1) and f(2) and it worked. Then I tried to substitute k+1 for x but I have gotten stuck.
Click here to see answer by richard1234(4789) |
Question 527290: Prove : If m is an odd integer, then 4 divides m^2 +2m+5
I have gotten this so far but i dont know if its right and how to finish working it out!
Proof: Let m be an odd integer
there is an integer such that m=2k+1
then m^2 +2m +5 = (2k+1)^2 + 2(2k+1) +5
then m^2 + 2m +5= (4k^2 +4k +1) + (4k+2) +5
then m^2 +2m +5= (4k^2 +4k+4k) +1+2+5
then m^2 +2m +5 = 4(k^2 +k+k) + 8
Click here to see answer by richard1234(4789) |
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(48502) |
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 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(6929)  |
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(4789) |
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(4789) |
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(6929) |
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(4789) |
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 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(12114)  |
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