Questions on Logic: Proofs answered by real tutors!

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Question 297358: could you please help me construct a proof for this argument?
1. A <--> B conclusion ~B <--> ~A
Click here to see answer by jim_thompson5910(35256)

Question 297357: I'm stumped on this problem, could someone please help me construct a proof?
1. (G * P) -> K
2. E -> Z
3. ~P -> ~Z
4. G -> (E v L) conclusion is (G * ~L) -> K
Click here to see answer by jim_thompson5910(35256)

Question 297356: Could you please help me construct a proof for this problem?
1. (G -> H) -> J conclusion is H -> J

Click here to see answer by jim_thompson5910(35256)

Question 297747: Construct a truth table for ~p --> (p ^ ~q)
Click here to see answer by user_dude2008(1862)

Question 298840: 1. ~J v ~L
2. ~(J * L) -> ~M
3. ~E v (M v ~S) / ~(S * E)
Click here to see answer by jim_thompson5910(35256)

Question 301507: csc2x+cot2x=cotx
Click here to see answer by Alan3354(69443)

Question 302702: Derive the conclusion of the following symbolized argumet.
1. T>[(A*R)>(Sv~A)
2. ~S /(T*R)>~A
Click here to see answer by jim_thompson5910(35256)

Question 309031: A v B
Click here to see answer by Fombitz(32388)

Question 309545: Let p, q, and r be the following statements: show work

p: Jamie is on the train.
q: Sylvia is at the park.
r: Nigel is in the car.

Translate the following statement into English: (~r V q)(right arrow)~p
Click here to see answer by alicealc(293)

Question 309542: Write a negation of the statement.
Some photographs are not displayed at this exhibition.
(A) All photographs are displayed at this exhibition.
(B) No photographs are displayed at this exhibition.
(C) Some photographs are displayed at this exhibition.
(D) All photographs are not displayed at this exhibiti
Click here to see answer by alicealc(293)

Question 310154: Prove the following conjecture:
"The sum of any three positive consecutive odd integers will be divisible by three."
This is urgent! Thank you!
Click here to see answer by Alan3354(69443)

Question 312401: Seattle Greenery: In July in Seattle, the grass grows � in a day on a sunny day and � in a day on a cloudy day. In Seattle in July, 75% of the days are sunny and 25% are cloudy
a.) Determine the expected amount of grass growth on a typical day in July in Seattle.

b.) Determine the expected total grass growth in the month of July in Seattle.

Click here to see answer by Theo(13342)

Question 313546: What is 50(N^2)? That is my original question.
I am trying to create a proff for a number trick.
this is what I have so far.
example
Choose a number 2
multipy it by 2 2(2)= 4
then add 5 4+5= 9
multiply by 50 50(9)= 450
add 1760 450+1760= 2210
subtract 1980 2210-1980= 230
My Proof:
N
2N
2N+5
50(2N+5)=100N+250
100N+250+1760= 100N+2010
100N+2010-1980= 100N+30
I am stuck after this point. The example answer is correct. I am suppose to end up with the original number plus my age and I did. Now, considering that I already know what N is my proff is actually still correct but it is incomplete and I don't know what to do from here. The idea is that it should work if any number was used. I assume my final proff should look something like this N and 30 with N representing 200 although it is really supposed to just be 2.
I want to show you the original problem.
PROBLEM:
1) Choose a number from 1 to 7, which represents the number of times you would like to eat dinner out each week (one per day).
2) Multiply this number by two.
3) Then add five.
4) Multiply this result by 50.
5) Now, if you have had your birthday this year already, add 1760 to the result in step 4. If not, add 1759
6) Then subtract your birth year.
The resulting number is a three-digit number. The first (leftmost) digit gives the number of times you would like to eat out each week. The other two give your current age.
INSTRUCTIONS: What I am supposed to do is:
1) Do a couple of examples with different numbers of dinners to get the feel of the process; Show these in your answer.
2) Construct a formal, �symbolic,� deductive reasoning proof for it, as seen in class with other problems (like we did with the number tricks) where you will introduce symbols and (a VERY small amount of) algebra along with your reasoning.
3) This is NOT a computation problem only, but mostly it is. It is not difficult, but you will need to play around with it.
4) You need to explain and show in mathematical terms clearly how and why the three-digit number gives you the dinner and the age.
5) I suggest that you use N for the number of dinners, and 19xy for your birth year. Be sure to clearly and specifically state how your age develops in the answer as the last two digits and why/how the number of dinners is first. This is where the credit is earned in particular.
I am on question 2, simply trying to create my proff. I hope that you can help.
Click here to see answer by stanbon(75887)

Question 316781: Will someone please show me how to find the derivative of the following function:
f(x) = x^6 + x^4 + 1
A solution with full working and steps would be much appreciated.
Thanks -Nick.
Click here to see answer by moshiz08(60)

Question 321292: X and Y are the different numbers selected form the first fifty counting number from 1 to 50 inclusive. What is the largest value that X+Y divided by X-Y can have?

Click here to see answer by jim_thompson5910(35256)

Question 331646: I am using the fitch program and trying to solve this proof:
1. A V B
2. A V C
-----
A V (B ^C )

I am having to use nested subproofs. I am to the very end and can't seem to figure it out!
Click here to see answer by Edwin McCravy(20055)

Question 332289: I'm a bit confused about logic proofs and I'm not sure if I'm doing this right. Any help would be greatly appreciated.
Derive the conclusions of the following symbolized arguments using natural deduction.
1. E > (A ∙ C)
2. A > (F ∙ E)
3. E / F

(Here is what I've come up with so far. I'm not sure whether I'm doing this correctly or not).

4. (A ∙ C) 1,3,MP
5. A 4,simp
6. (F ∙ E) 2,5.MP
7. F 6,simp

Click here to see answer by jim_thompson5910(35256)

Question 332293: Please help me to derive the conclusion of the following using natural deduction. I'm not really sure what I'm doing on this one as far as double addition, etc.
1. (S > Q) ∙ (Q > ~S)
2. S v Q
3. ~Q /P ∙ R (hint: proof requires use of addition)
Click here to see answer by jim_thompson5910(35256)

Question 335913: Given: Two concentric circles with tangent to smaller circle at R
Prove: AR = RB
Click here to see answer by Edwin McCravy(20055)

Question 338564: What will be the basis step for the sum of the first n odd integers. Explain the solution.
Click here to see answer by Edwin McCravy(20055)

Question 341634: Show that the square of any odd integer is odd. Use this fact to justify the statement "if p� is even, then p is also even".
Click here to see answer by Edwin McCravy(20055)

Question 349548: Prove the following statement.
If n=m^3-m for some integer m, then n is a multiple of 6.

My work so far:
Suppose n=m^3 - m. Thus n=m(m-1)(m+1). First if m=2k for some integer k. Thus n=(2k)(2k-1)(2k+1)= 2 (k(2k-1)(2k+1)). Also if m=2k+1 for some integer k, then n=(2k+1)(2k)(2k+2)=2(k(2k+1)(2k+2))
Thus n is divisible by 2.
I would like to find out how n is also divisible by 3 because if n is divisible by 3 as well then n would be divisible by 6.
Click here to see answer by jsmallt9(3758)

Question 350522: Give a proof of the following argument:
1 (1) A --> (B & ~K) Premise
2 (2) (B & ~K) --> ~A Premise

Conclusion: ~A v G
I have absolutely no idea what to do. Please help me, please!
Click here to see answer by jim_thompson5910(35256)

Question 353557: Tom always tells the truth, Dick sometimes tells the truth, and Harry never tells the truth. On the way to a masquer-ade party, the one dressed as Bob Dole says Tom is Bill Clinton." The one dressed as Bill Clinton says I'm Dick."
The one dressed as Ross Perot says Harry is Bill Clinton." The man dressed as Bill Clinton is:
(a) Tom (b) Dick (c) Harry (d) Either Tom or Dick
(e) None of the above

Click here to see answer by vleith(2983)

Question 353568: Show that
if(~Pv~Q)then (~P&~Q)
is equivalent to
if (PvQ) then (P&Q)
Click here to see answer by Edwin McCravy(20055)

Question 358447: Proof that the square of even number is even number
Click here to see answer by ewatrrr(24785)

Question 358446: Proof that the sum of two even numbers is even
Click here to see answer by ewatrrr(24785)

Question 332741: 1) THE RATE OF COLOR TONER INCREASES $33 TO $35 AND THE RATE OF BLACK WHITE TONER INCREASES $28 to $29 . IF THE COMPANY SPENDS $1540 IN WHICH 3/5 IS COLOR TONER THEN HOW MUCH IS TOTAL EXPENDITURE INCREASES AFTER COST HIKE?

2)Company A taken a truck on rent of $1280 per month another company B bought the truck in $40000 and send $120 per month. After 4 years what will be the difference in the amount spent by the both companies on the TRUCK.?
Click here to see answer by lavakumark(1)

Question 361025: prove: if t>0, there exists b such that if x>b then (1/(sqrt(x))) < t
Click here to see answer by robertb(5830)

Question 361792: I'm not positive how to write the symbols on a computer so hopefully I do this right. I need help doing the proof of: (P^G)⇒R, (R^S)⇒T, P^S, G∨R /(therefore) R∨T. Thanks!
Click here to see answer by solver91311(24713)

Question 361802: Please help me solve this proof: ~C⇔A, (F^H)∨~C, ~(A∨B) /(therefore) F^~B. Thank you!
Click here to see answer by solver91311(24713)

Question 362773: If you add a 10% sales tax increase will that benefit or hurt the economy?
Click here to see answer by Manny Pacquiao(82)

Question 362883: Use cases to prove that x^2+x-1=0 has no rational solutions.
Click here to see answer by Fombitz(32388)

Question 363694: how can you prove the conclusion A v ~~B from the premise A v B?
Click here to see answer by Fombitz(32388)

Question 365893: Prove: abs(xy)= abs(x)*abs(y)
Click here to see answer by robertb(5830)

Question 366128: hello i need help with a some logic proofs that i do not understand
Click here to see answer by solver91311(24713)

Question 369957: if f(x)=2x
show that f (x + 4)-f(x-2)=63/4
if f(x,y) = x4 + 3x2 y2 + y4
show that f (ax,ay)= a4.f(x,y)
Click here to see answer by jim_thompson5910(35256)

Question 373128: How would you go about doing (1+cosx+sinx)/(1+cosx-sinx)=secx+tanx ?

Click here to see answer by CharlesG2(834)

Question 374237: I am having trouble solving the following propositional logic proofs.
1. Conclusion: N + Y
1. K > (N & P)
2. S > (X & Y)
3. S + K
2. Conclusion: ~Q > ~M
1. M > [ Q + ~(E + H) ]
2. ~E > H
3. Conclusion: A & D
1. ~D > (F & P)
2. ~A > ~(F + P)
3. (F <=> P) > (~~D & A)
4. Conclusion: F > (Y > F)
1. Q
5. Conclusion: ~(~Q > ~X) > ~J
1.J > (M > Q)
2. X > (M + V)
3. J > (V > ~X)
Click here to see answer by jim_thompson5910(35256)

Question 380057: Can I get help solving A v ~~B from A v B
Click here to see answer by jim_thompson5910(35256)

Question 384304: I need a Formal Logic Proof for the following (I know that it is valid):
(P1) X⊃(X�Y)
(P2) [(X�Y)∨(~X�Y)]⊃Y / Y⊃Y

*I am aware that there are many different variations on the symbols, etc. used in formal logic, so below are the symbols we use in class:
~ negation
∨ or
� and
≡ if and only if
⊃ if ... then
Click here to see answer by jim_thompson5910(35256)

Question 384302: I need a Formal Logical Proof for the following (I know it is valid):
(P1) ~(A≡B)
(P2) ~(B≡C) / A≡C

*I am aware that there are many different variations on the symbols, etc. used in formal logic, so below are the symbols we use in class:
~ negation
∨ or
� and
≡ if and only if
⊃ if ... then
Click here to see answer by jim_thompson5910(35256)

Question 385424: Consider the following argument"

If you cannot eat peanuts then you are allergic.
If you are allergic then you have health problems.
You have health problems.
Therefore, you cannot eat peanuts.
Is the argument valid, or invalid?
Click here to see answer by richard1234(7193)

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