Questions on Logic: Proofs answered by real tutors!

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Question 9013: How can you prove that:
odd + odd = even
even + even = even (you initially put even + even = odd)
odd + even = odd
????
Click here to see answer by prince_abubu(198)

Question 9163: How do you prove that 5 is a prime number?
Click here to see answer by bonster(299)

Question 9579: If x is an integer, x is even if x=2p for some integer p, and x is odd if for no integer p such that x=2p. If ab is an odd number, show that a and b are both odd.
Click here to see answer by prince_abubu(198)

Question 7704: suppose G is the set of all functions from ZtoZ with multiplication defined by composition, i.e,f.g=fog.show that f has a right inverse in G IFF F IS SURJECTIVE,and has a left inverse in G iff f is injective.also show that the setof al bijections from ZtoZis a group under composition.
Click here to see answer by khwang(438)

Question 12118: The hypotenuse of a certain right triangle has length 185 and one of its legs
has a length of 57. Find the length of the other leg. Decide whether the answer is exact or just a very good approximation.
To solve the first part of the problem, I used the pythagorean theorem, making the length of the other leg √30976= 176. How do I prove that this is exact or just an approximation?
Click here to see answer by rapaljer(4671)

Question 12328: Where did I go wrong? Please giveme the corrected answer.
Given m=n
Multiply m2=mn
Subtract m2-n2=mn-n2
Factor/Multiplication (m-n)(m+n)=mn-n2
Factor/Multiplication (m-n)(m+n)=(m-n)n
Divide m+n=n
Subsitute n+n=n
Addition 2n=n
Divide 2=1

Click here to see answer by kusha(21)

Question 18663: I don't know how to solve this two logic proofs, please help!
(A→B)→A ├ A
and
├ (A→B) v (A→ �B)
Click here to see answer by khwang(438)

Question 24525: Somebody please help me with this problem... and thank you in advance!!
Square ABCD with sides 2 units long is constructed in a semicircle with radius r and diameter PQ.
a) Determine the radius of the circle
b) Show that rectangle ABQR is a golden rectangle
Click here to see answer by Earlsdon(6294)

Question 24523: Somebody please help me with this problem... and thank you in advance!!
USING DEDUCTIVE REASONING
There are 9 significant points associated with a triangle that always lie on a circle. These points are:
- the midpoints of the sides: D, E, F
- the feet of the altitudes: P, Q, R
- the mipoints of the segments joining the orthocentre, H, to the three vertices: X, Y, Z
a) Prove that quadrilaterals FEZY and DEXY are rectangles
b) Expain why the result of part a) proves that D, E, F, X, Y, and Z all lie on the same circle.
c) Why do the points P, Q, and R also lie on this circle?
d) Complete a proof that D, E, F, P, Q, R, X, Y, and Z lie on a circle. This circle is called the nin-point circle of the triangle.
Click here to see answer by venugopalramana(3286)

Question 28516: I came across this IQ question:
How do you proof that 10 = 9.999999999...?
Click here to see answer by venugopalramana(3286)

Question 43127: Is the squ rt of x (squared) = x an identity (true for all values of x)?
Explain
Click here to see answer by fractalier(6550)

Question 54107: Consider the following statements
All United States Postal workers are federal employees
Jim is a United States postal worker
Write the first statement as a conditional and use deduction to show that John is a federal employee.Draw an Euler diagram to illustrate the logic of your deduction.
Click here to see answer by funmath(2933)

Question 56086: . Find the ABSOULUTE EXTREMA of f(x)= x ^4/3 on the interval
> [-1,8].
> Use the EVT (Extreme Value Theorem)

Click here to see answer by stanbon(75887)

Question 56092: > 3. The function f(x)= (x^2+2x)^2/3: (USE CALCULUS to answer a-e)
>
> a. Increasing on what interval(s)
> b. Decreasing on what interval(s)
> c. Has critical numbers?
> d. Has Relative Maximum?
> e. Has Relative Minimum?

Click here to see answer by stanbon(75887)

Question 56888: f(x)=x^4-18x^2+4

Find all the points of inflection.
Please help!

Click here to see answer by Scriptor(36)

Question 57281: Please Please Help!
Find all the points of inflection (concavity)
f(x)= x^4-18x^2+4
Click here to see answer by funmath(2933)

Question 57283: This is a calculus question:
Please Please Help!
Find all the points of inflection (concavity)
f(x)= x^4-18x^2+4

Click here to see answer by stanbon(75887)

Question 60609: I am 38 years old and I don't remember this stuff too well.
I know Z=(Y+X)/X
and X=Y/(Z-1)
I have been moving these variables around and can't remember how I got the solution for X from the first equation. Please help in refreshing my memory.

Click here to see answer by ankor@dixie-net.com(22740)

Question 60483: what is the range of 17,23,5,13,12
Click here to see answer by 303795(602)

Question 62873: Can you prove if the quadrilateral is a parallelogram then opposite sides of a quadrilateral are congruent?
Click here to see answer by venugopalramana(3286)

Question 66567: Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart?
Hint: This is different from problem #3, because we do not know the total distance. We do know that one car is 180 miles ahead of the other, so the slow car's distance can be represented by " d " and the distance of the fast car, which would be ahead, can be represented by "d + 180." The time is the same again, and can be represented by "t." This time we have two unknowns, so we need two equations, one for the fast car, and one for the slow car. Again we are using the basic formula d = rt , and substituting the values that are relevant to our situation. The equation for the slow car is: d = 55t. You write the equation for the fast car, and solve the system by substitution. Don't forget the units in your answer.
Click here to see answer by venugopalramana(3286)

Question 69325: What would be the couterexample to the statement below?
If the sum of two integers is even, then both of the integers are even.
Click here to see answer by bucky(2189)

Question 74408: Prove that for any sets A and B, if A is a subset of B, then
Help! Thanks!
Click here to see answer by maamarmath(1)

Question 83901:
Click here to see answer by Nate(3500)

Question 97605: I want to know the next four letters of this pattern: T,F,S,N,E,T
Click here to see answer by Earlsdon(6294)

Question 99157: How do you construct a formal proof for the following argument:
A ^ (B v C) to conclude with the goal, (A ^ B) v (A ^C)?
Click here to see answer by Adam(64)

Question 98350: prove that 1+3sqrt(3) is irrational
1 + 3* 1.732050808
1+ 5.196152423
6.196152423
Click here to see answer by scottnascar(12)

Question 104112: Given angle 1 is =(squiggly line on top of the equal sign) to angle 2
and angle 3 ia =(squiggly line on top of the equal sign) to angle 4
Prove: a is parallel to c
there's a picture and here's a description of what it looks like:
There are 3 horizontal lines, line a is the top most one, line b is in the middle, and line c is the bottom most one, (theses are all horizontal)
Then there are 2 vertical lines going through all three of the horizontal lines. (these vertical lines are kind of slanted).
In between line b and c, there are the numbers 1 and 2. Number 1 is on the left of the vertical line that is closest to b and c and it is under line b in the top left side of the vertical line. and number 2 is the opposite of number 1,(i think these are alternate interior angles or numbers).
Then there's a number 3 located on the other vertical line, that is going through line a. the number 3 is on top of line a, and to the right of the second vertical line going through all three horizontal lines.
Lastly number 4 is located under line b, but to the right of the 2nd vertical line. So that it is corresponding to number 1.
Please help me prove this problem.
Click here to see answer by elima(1433)

Question 122291: 12. A particle of mass 2kg slides down a rough plane inclined at 20 degrees to the horizontal. Given that the acceleration of the particle is 1.5ms-2, find the coefficient of friction between the particle and the plane.
Thanks for any help, its so hard :D
Click here to see answer by Fombitz(32388)

Question 122289: I didnt know what topic this stuff came under, :( so i thought proof maybe....the closest i can find, its a mechanics question.
11. A parcel of mass 60kg is released from rest on a smooth plane inclined at arcsin 0.6 (3/5) to the horizontal. Find the velocity of the parcel when it has travelled 5m down the slope.
I cant do it, can some one help?
What i personally did was,
invsin0.6 = 37, Sin37*9.81*60 = 354 approx.
So Acceleration down the slope is 354ms-2,
v squared = u sqaured + 2as,
so, velocity squared therefore =, 2 * 354 * 5 = 3540, root that = velocity, =59.5...
but the answer is 7.67 :( Please help? with details of how to do, thanks.
Click here to see answer by scott8148(6628)

Question 123516: Prove that there is a positive integer that can be written as the sum of squares of positive integers in two different ways.
Click here to see answer by Edwin McCravy(20054)

Question 123519: Assuming the truth of the theorem that states that √n is irrational whenever n is a positive integer that is not a perfect square, prove that √2 + √3 is irrational.
Click here to see answer by Edwin McCravy(20054)

Question 127064: Show that the sum of an odd integer and an even integer is an odd integer
Click here to see answer by josmiceli(19441)

Question 128145: Please assist me in arriving to the answer of this problem.
The problem as stated from the book:
Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.
Given hint by professor:
Either use contradiction or better yet try proof by cases.
I do not understand how to use proofs by contradiction.
Click here to see answer by ozymandias(9)

Question 131383: i need help on this question please.
Click here to see answer by TakeATuition.com(57)

Question 136047: Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.

You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat � at random � on the head of each. Then you hide the other two hats and remove the blindfolds.

You then ask each genius to name the color of his hat (which he cannot see).

The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."

WHAT COLOR IS THE FRONT GENIUS' HAT??????

Click here to see answer by jonessk(1)

Question 141682: How many combinations of room decoration can you create with 12 wall papers, 7 floors and 5 drapes? What equation do I need to use to solve this problem? What would be the proof?
Click here to see answer by checkley77(12844)

Question 144253: PLEASE HELP !!!!!
In using mathematical induction to prove 1^2+3^2+5^2=...+(2n-1)^2 =
(n(2n-1)(2n+1)/3), the P k statment is 1^2+3^2+5^2+...+(2k-1)^2 = (k(2k-1)(2k+1)/3)
Is this true or false
THANK YOU
Click here to see answer by stanbon(75887)

Question 145211: Could you help me with this Please?
9. (6 pts) A couple plan to have exactly three children.
(a) Construct a tree diagram and list the sample space.
View this --> http://collabvsl.wetpaint.com/page/Basic+Probability
(b) Find the probability that the family has at least two girls.

Click here to see answer by vleith(2983)

Question 145216: I need your help here-please
14. (2 pts) How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview? 19 * 7 at a time = 19*18*17*16*15*14*13
I am not that strong in this field. Can you look over this stuff AND get me the answers when it is done so I know where i may have goofed up?
Click here to see answer by jim_thompson5910(35256)

Question 145210: I am not sure of this answer; is it corret?
Thank you!
5. (3 pts) 500 raffle tickets are sold at $2 each. One grand prize of $100 and two consolation prizes of $50 will be awarded. Find Jake�s expectation if he purchases one ticket.
100(1/500) + 50*(2/500) � 2*(497/500) = (200-994)/500 = - 1.58
A) -$0.40 B) -$1.20 C) -$1.60 D) $7.75 E) $0.80

Click here to see answer by jim_thompson5910(35256)

Question 145212: Could you please help me with this? Thank you
1000 tickets for prizes are sold for $2 each. Seven prizes will be awarded � one for $400, one for $200, and five for $50. Steven purchases one of the tickets.
400(1/1000) + 200(1/1000) + 50(5/1000) � 2(993/1000) = -1.14
a) Find the expected value expected value is -$1.14
b) Find the fair price of the ticket. ?????

Click here to see answer by jim_thompson5910(35256)

Question 145213: I can't figure this. Can you help me.
7. (2 pts)
Two balls are to be selected without replacement from a bag containing one red, one blue, one green, one yellow, and one black ball. How many points are there in the sample space? 5*4 = 20 ??

Click here to see answer by scott8148(6628)

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