Questions on Logic: Proofs answered by real tutors!

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Question 1045663: 3. Let f(x) =x + 2p if x < −2, 3px + q if −2 ≤ x ≤ 1, 3x−2q if x > 1. Determine the values of p and q that make f continuous
Click here to see answer by robertb(5830)

Question 1046327: PLEASE HELP ME!
Proof by math induction (2n-1)^3= n^2(2n^2-1)
I am pretty sure it is true but I don�t know how to prove it. Thanks
Click here to see answer by ikleyn(52775)

Question 1046346: Using mathematic Induction to prove the next proposition:
1^3 + 3^3 + 5^3 +... + (2n-1)^3 = n^2(2n^2 - 1)
Click here to see answer by ikleyn(52775)

Question 1046573: please help me by showing the proof of the following using the rules of replacements..This propositions are logically equivalences and I need to see the proofs..thank you..
1. (P v Q)=>R = (P=>R)^(Q=>R)
2. P v (P^Q) = P
3. P ^ (PvQ) = P
Click here to see answer by robertb(5830)

Question 1046473: Help me to understand what this means {(a,b)|a,b∈R} and how to apply it to proofs for the vector laws and scalar multiplication laws?
Click here to see answer by richard1234(7193)

Question 1046927: Can anyone help with this?
Prove using mathematical induction that, for all n ∈ N,
1 − 2 + 3 − 4 + � � � + (−1)n+1n =

(n + 1)/2, when n is odd,
−n/2, when n is even.
Thanks very much
Click here to see answer by ikleyn(52775)

Question 1046926: Can someone help with this?
Let σ be the relation on N defined by x σ y if and only if x ≤ y ≤ 2x.
Prove that σ is reflexive
Is σ transitive?
thank you very much
Click here to see answer by rothauserc(4718)

Question 1047975: Complex numbers
If z=rcis(theta) FIND: |iz^2|
I am confused about how I incorporate the i into the absolute value. I can't remember what it means. Please help and show exactly how I complete the workings. I can easily find the absolute value of z^2 I just really don't understand how to put the i into it.
Thank you!!
Click here to see answer by ikleyn(52775)

Question 1049114: The question is to proof P = P and all the following rules must be involved: &out, ->in, &in, and ->in
Click here to see answer by solver91311(24713)

Question 1049126: Our teacher asked us this question today and we were asked to figure it out but no one was able to, so I'm asking someone better than me at this. Here is your problem.
1+2=3
1+2=4
1+2=5
All solutions are true how is this possible?
Click here to see answer by ikleyn(52775)

Question 1049124: 1+2=3
1+2=4
1+2=5
All solutions are true how is this possible?
Click here to see answer by ikleyn(52775)

Question 1049359: 1/8 of 9 number is 6 the answer is 128 how???
Click here to see answer by stanbon(75887)

Question 1050042: how to proof 8x - 12y = 14 has no integral solution in x and y
Click here to see answer by Edwin McCravy(20054)

Question 1049441: Prove:
Premise: Mv(N->M)
Conclusion: ~M->~N
Click here to see answer by robertb(5830)

Question 1050795: Good morning sir's and ma'ams..Kindly help me answer the following:
Construct a formal proof of validity for each argument..
1. A => B
A v (C ^ D)
-B ^ -E
Therefore C.
2. W => X
(W ^ X)=>Y
(W ^ Y)=>Z
Therefore W => Z.
Click here to see answer by robertb(5830)

Question 1050201: Prove that the following two arguments are valid using the method of Natural Deduction. Show your work, which means �do the proofs just like Hurley does them.� Note that �//� is used as a conclusion indicator.

1. (R & I)
2. [(R v G) -> Z] // (Z v ~W)
Click here to see answer by robertb(5830)

Question 1052276: Hi I'm kind of stuck on this:

We have seven different pairs of shoes, and eight different pairs of socks.
(a) How many ways are there to pick a pair of shoes and a pair of socks?
for this I think its just 7 choose 1 * 8 choose 1
= 56
(b) How many ways are there to pick a pair of shoes and two socks, not necessarily from
the same pair? (Socks in the same pair are identical, but socks from different pairs are
different.)
How would I go about this what I have so far is 7 choose 1 * 16 choose 2 * 15 choose 1
= 12600
It seems like too large a jump?
Thanks
Click here to see answer by addingup(3677)

Question 1052740: Good morning ma'am/sir:
I need your help for the following problems on quantification.
Instructions: Let the universe of discourse in each case be the set of natural numbers.Determine the truth value. If true,prove it. If false,provide a counterexample.
1. For all x there exist y such that (x < y)
2. There exist x for all y such that (x < y)
3. There exist x for some y such that (x < y).
Please help me. Thank you!
Click here to see answer by KMST(5328)

Question 1053002: What are the amounts of postage that can be made with an unlimited supply of 5-cent and 8-cent stamps?
Click here to see answer by KMST(5328)

Question 1053445: Use mathematical induction to prove each of the following:
Fore each natural number n, 3 divides (4^(n)-1)
Click here to see answer by richard1234(7193)

Question 1054668: if this is december,then last month was november.if last month was was november,then six months ago it was june.if six months ago it was june,then eleven months ago it was january.if next month will be january,then this is december.last month was november.Therefore, this is december{D,N,J,A,X}.Sir, please guide how to check the validity of this argument.THIS PROBLEM is on my agenda since a few years. Please Help.
Click here to see answer by Fombitz(32388)

Question 1056542: prove validity using inference rules and rules of replacement and say which rule was used at each step:
1)
1. {X+[Y+(~(A.F)>B)]}
2. (X>C)
3. (Y>C)
4. {~B.[Z.(~C+~C)]}
5. /(F.Z)
2)
1. (A+C)+(A+B)
2. (A+(B+C))>D
3. /D
3)
1. (A>C)+(B>D)
2. /(A.B)>(C+D)
Click here to see answer by Edwin McCravy(20054)

Question 1058597: What would the completed formal proof be?
1. M * (L v P)
2. ~M v ~L :. M * P
3.
4.
Click here to see answer by Edwin McCravy(20054)

Question 1058601: Can you help me solve this formal proof?
1. (C * K) v (L * T)
2. ~C v ~K :. L * T
3.
4.
Click here to see answer by Edwin McCravy(20054)

Question 1058600: Can you tell me the completed formal proof?
1. (C v D) > (E * F)
2. D v C :. E
3.
4.
Click here to see answer by Edwin McCravy(20054)

Question 1059930: Using rules of implication, need help with the proofs!

1. T -> (P v Q) 2. S v ~(P v Q) 3. ~S | ~T

Thanks for your help!

Click here to see answer by solver91311(24713)

Question 1059940: Looking for a logical proof help using rules of implication! Thank you!

1. (S ⊃ R) � Q 2. R ⊃T | S ⊃ T

Click here to see answer by solver91311(24713)

Question 1060015: Need help with these proofs using rules of implication! Thank you!
1. P v (T v R)
2. T ⊃ S
3. R ⊃ Q
4. ~P /S v Q
Click here to see answer by Edwin McCravy(20054)

Question 1060024: Proof using rules of replacement. Thanks for your help.
1. G � K
2. K ⊃ E
3. E ⊃ (G ⊃H) /H

Click here to see answer by Edwin McCravy(20054)

Question 1060006: Looking for a logical proof help using rules of implication! Thank you!
1. [(T � R) v S] ⊃ (P v Q)
2. T
3. R /P v Q

Click here to see answer by Edwin McCravy(20054)

Question 1060029: Using rules of implication and replacement- proof
1. M v (D � L)
2. B ⊃~(M v L) /~B
Thank you!!
Click here to see answer by Edwin McCravy(20054)

Question 1060034: Proof using rules of implication and replacement.
1. T v S
2. ~T
3. (S v S) ⊃ (~P v R) /~R ⊃~P
Thank you!!
Click here to see answer by Edwin McCravy(20054)

Question 1060045: Using a conditional proof:
1. (D v E) ⊃ (F � G)
2.( A v B) ⊃ (D � C) /A ⊃ F
Thank you.
Click here to see answer by jim_thompson5910(35256)

Question 1060204: Using an indirect proof to solve this problem:
1. B ⊃ (C ⊃~B)
2. A ⊃ (B ⊃ C) /~A v ~ B

Thank you!

Click here to see answer by jim_thompson5910(35256)

Question 1060710: Can you solve:
1. T / S > T
Click here to see answer by ankor@dixie-net.com(22740)

Question 1061182: 1. (N v M) > (P & O)
2. ~M > (~Q > Q)
3. ~O
/Q
Click here to see answer by jim_thompson5910(35256)

Question 1061179: 1. (I v K)>~L
2. (H v J) >I
3. ~K
4. H v K
/~L
Click here to see answer by jim_thompson5910(35256)

Question 1061177: 1. (~F&E) > (G>F)
2. F>~E
3. E
/~G

Click here to see answer by jim_thompson5910(35256)

Question 1061189: 1. (I v K) > ~L
2. (H v J) > I
3. ~K
4. H v K
/~L
Click here to see answer by jim_thompson5910(35256)

Question 1061188: 1. (~F & E) > (G > F)
2. F > ~E
3. E
/~G
Click here to see answer by jim_thompson5910(35256)

Question 1061347: i need help for the following ,,,need to construct a formal proof for the following valid arguments..
~ w → ~ a
~ ( w ٨p ) V s
S →b
~ (a ٨~ p)
_______________
a →b

Click here to see answer by Edwin McCravy(20054)

Question 1061555: ~b → ~r
e → (f → y)
~(e → y)
f V (m V r)
____________
m V b
Click here to see answer by math_helper(2461)

Question 1061571: ~ w → ~ a
~ ( w ٨p ) V s
S →b
~ (a ٨~ p)
_______________
a →b

Formal proof written form
Statements and their reasons
Click here to see answer by Edwin McCravy(20054)

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