Questions on Logic: Proofs answered by real tutors!

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Question 927239: Complete the following proofs, choosing from among the first four Rules of Implication:
(1) A>(B>D)
2. A>~C
3. Cv~D
4. A / ~B

Click here to see answer by AnlytcPhil(1806)

Question 928249: I am having trouble solving this proof:
1. DvM
2. M-->R
3. Sv(Q&X)
4. R-->~S
5. ~D /Q
So far I have:
6. M
7. R
8. (M&R)
Is this correct so far? This is the farthest I have gotten and don't quite understand how to solve the rest of this proof. Any help would be greatly appreciated. Thank you!
Click here to see answer by AnlytcPhil(1806)

Question 929849: 1. A -> (D -> E)
2. F -> [(A & B) v (A & ~B)]
concl: (F & D) -> E
Professor says it is 11 lines w/ CP.
HELP ME.

Click here to see answer by Edwin McCravy(20055)

Question 929683: prove that the sum of all natural numbers divisible by 5 is equal to 5n(n+1)/2 using mathematical induction.
Click here to see answer by Edwin McCravy(20055)

Question 929929: I need the following proof :) PLEASE. I am struggling...
1. P-> (~Q & R)
2. (Qv~R) ->S
3. ~SvP
Conclusion: ~Q
THANK YOU!
Click here to see answer by Edwin McCravy(20055)

Question 928737: Complete the following proof, choosing from among the first eighteen Rules of Inference and Replacement rules.
1. C  (~L  Q)
2. L  ~C
3. ~Q

Click here to see answer by Edwin McCravy(20055)

Question 928685: Please help me solve 1. h -> ~a
2. a
// ~(h v ~a)
Click here to see answer by Edwin McCravy(20055)

Question 928647: I need to somehow get "R ≡ ∼Q" as the conclusion, using natural deduction (This means the 18 rules of natural deduction, Modus Ponens, Modus Tullens, De Morgan's Rule etc etc.)

Conclusion: R ≡ ∼Q
1. A ⊃ (Q ∨ R)
2. (R � Q) ⊃ B
3. A � ∼B
Click here to see answer by Edwin McCravy(20055)

Question 929923: Can anyone annotate the following proofs for me?
Proof 1:
1. (AvB) -> C
2. (CvD) -> E
3. CvA
4. ~C .: E
5. A
6. AvB
7. C
8. CvD
9. E

Proof 2
1. X->Y
2. X->Z .: X-> (Y&Z)
3. ~XvY
4. ~XvZ
5. (~XvY) & (~XvZ)
6. ~Xv(Y&Z)
7. X-> (Y&Z)
Proof 3
1. ~(A&(BvC)) .: A -> ~B
2. ~((A&B)v(A&C))
3. ~(A&B) & ~(A&C)
4. ~(A&B)
5. ~A v ~B
6. A -> ~B
PLEASE and thank you!!!! I need lines and rules.
Click here to see answer by Edwin McCravy(20055)

Question 928684: Please help me solve 1. (~m>p) * (~n>q)
2. ~(m*n)
// P v Q
Click here to see answer by Edwin McCravy(20055)

Question 928646: I need to somehow get ~K as the conclusion, using natural deduction (This means the 18 rules of natural deduction, Modus Ponens, Modus Tullens, De Morgan's Rule etc etc.)

1. K ⊃ L
2. ∼K ∨ F
3. (L � F) ⊃ A
4. ∼A
Click here to see answer by Edwin McCravy(20055)

Question 928682: Please help me solve 1. n> (j>p)
2. (j>p)>(n>p)
3. n
// p
Click here to see answer by Edwin McCravy(20055)

Question 931273: what color is my underwear?? I forgot
Click here to see answer by richard1234(7193)

Question 932733: Can someone please help me with this proof using the 18 rules of inference?
> is a horshoe, v is the wedge, * is the dot
1. (S v T) > (S > ~T)
2. (S > ~T) > (T > K)
3. S v T Therefore: S v K
4. S > ~T 1,3 Modus Ponens
5. T > K 2,4 Modus Ponens
6. (S > ~T) * (T > K) 4,5 Conjunction
7. ~T v K 3,6 Constructive Dilemma
8. ~S v ~T 4, Material Implication
9. ~(S*T) 8, DeMorgan's Rule
I have been stuck on this question for hours, and I can't seek to get to S v K.

Click here to see answer by jim_thompson5910(35256)

Question 933035: prove that 1/n > 1/2power of n by using mathematical induction
Click here to see answer by richard1234(7193)

Question 934982: Premise : N > O
Conclusion : (N.P) > O
Provide formal proof of validity
Click here to see answer by Edwin McCravy(20055)

Question 934272: 1. ~R
2. S-> R/...(therefore) ~ S
Using the first 4 rules of inference: MP, MT, HS, DS
Include the premises in your proof
Click here to see answer by Edwin McCravy(20055)

Question 935274: This is a Number Theory proof:
If N = abc + 1, prove that (N, a) = (N, b) = (N, c) = 1.
(N, a) means "the greatest common divisor of N and a."
I have started the proof like this:
Let d = (N, a).
Since d = (N, a), then d | N and d | a. "d divides N" and "d divides a".

Click here to see answer by KMST(5328)

Question 935397: 1. ~P∨Q
2. Q→R ∴ P→R
1. R∨~Q
2. P→Q
3. ~R ∴ ~P
1. P
2. ~Q
3. ~R
4. (P&~Q)→(R∨S) ∴ S
1. (P&Q)→R
2. (P&R)→Q
3. P ∴ R↔Q
1. ~P&~Q
2. (P∨Q)∨(R∨S) ∴ (R∨S)
1. ~P ∴ ~(P&Q)
1. (P→Q)→S
2. S→~(T∨W)
3. (~T&~W)→R ∴ (P→Q)→R
1. (P&~Q)&(~R∨S)
2. ~((S&P)&~Q) ∴ ~R

1. P→Q
2. P→~(R∨Q) ∴ ~P

10. ∴ (P→~Q)↔(Q→~P)

Click here to see answer by Edwin McCravy(20055)

Question 935456: 1. A→B
2. A→~(C∨B) ∴ ~A
1. (A&~B)&(~C∨D)
2. ~((D&A)&~B) ∴ ~C

Click here to see answer by Edwin McCravy(20055)

Question 938725: complete the following proofs within the prescribed
Given: 2x+6=3+5/3x Prove: x=-9
Click here to see answer by stanbon(75887)

Question 938723: complete the following proofs within the prescribed
Given: 2x+6=3+5/3x Prove: x=9

Click here to see answer by stanbon(75887)

Question 942922: proof that 2=0
Click here to see answer by Alan3354(69443)

Question 943566: A donkey must transport 900 carrots to the market, which is 300 miles away. The donkey carries a maximum of 300 carrots, and eats 1 carrot every mile. What is the largest number of carrots that can be delivered to the market?
Click here to see answer by macston(5194)

Question 943569: A grandmother prepared bowls of fruits for her family. All but 5 are with cherries, all but 4 are with apricots, all but three are with red currants. How many bowls are there in total?
Click here to see answer by ptaylor(2198)

Question 943424: Prove (m+n)(p+q) = (mp+np) + (mq+nq)
I have already proved a proposition that states (m+n)p = mp + np, which matches up with part of the right side of the equation, but I'm not sure how to get to that point or how to incorporate mq+nq into it.
Click here to see answer by richard1234(7193)

Question 947081: |xy|=|x||y|
Click here to see answer by rothauserc(4718)

Question 947547: nCr/nCr-1 = (n-r+1)/r
prove it
Click here to see answer by Edwin McCravy(20055)

Question 949239: show the proof:
(P->Q) & (P->R)
conclusion:
P-> (Q&R)
Click here to see answer by Theo(13342)

Question 952302: Premise: ~(A->(B&C))
Conclusion: ~(A<->(B&C))
I've tried to Provisionally assume A<->(B&C), but I don't understand double arrow rules that well.
Click here to see answer by jim_thompson5910(35256)

Question 953371: Please help me by showing me how to do this problem and give me some tips on how to solve other problems like this : 1) If n^2˃4 and n is a natural number, then n ˃2
Thank you very much
Click here to see answer by Theo(13342)

Question 957000: Derive: R & M
1. ~(R & M) "if then symbol" (L & ~N)
2. N
Click here to see answer by jim_thompson5910(35256)

Question 957379: Boolean logic is the form of algebra in which all values are needed to either TRUE or FALSE normally through AND,OR and NOT operator.
a)How do the number of result change upon using an "AND" operator and an "OR" operator?EXPLAIN your answer with the help of relevant examples.
b)What is the name for the combination logic gate of an "AND" operator followed by a "NOT" operator?Explain the whole operation and provide the reasons on why do we need this combination.
Click here to see answer by Edwin McCravy(20055)

Question 957613: Premises: S v B , B⊃D, S⊃G
Conclusion: D v G
I am trying to work down from the premises but cant find way to get to the conclusion. Any help would be appreciated.
Click here to see answer by jim_thompson5910(35256)

Question 959411: why does an even number times an even number always equal an even product
Click here to see answer by rothauserc(4718)

Question 959729: Some things are caused to exist.
Anything caused to exist is caused by another [Nothing can bring itself into existence].
If some things are caused to exist and anything caused to exist is caused by another, then
either there�s a uncaused first cause or there�s an infinite series of past causes.
There�s no infinite series of past causes.
There�s an uncaused first cause.

Click here to see answer by Alan3354(69443)

Question 962579: Prove that when two odd numbers are squared and then added, the answer is always even.
Click here to see answer by Alan3354(69443)

Question 964275: (~RvD)-->~(F�G)/(F�R)-->S/F�~S/:.~(SvG)
Click here to see answer by Edwin McCravy(20055)

Question 962749: Can somebody please gimme a hand
1.�S -> Q
2.(U v P) -> (F v T)
3.(R & S) -> T
4.�R -> Q
5. Q -> U
concl: �T -> F
Click here to see answer by Edwin McCravy(20055)

Question 966638: Using Inference Rules
Premise 1. (P * Q) > R
Premise 2. (P * Q) V S
Premise 3. ~ R
Conclusion / S

Click here to see answer by Edwin McCravy(20055)

Question 966196: Please proof that:
sin^4x+cos^4x = 1-2sin^2xcos^2x
Click here to see answer by Edwin McCravy(20055)

Question 968066: odd+odd+odd=even
how to solve..plz tell me
Click here to see answer by josgarithmetic(39617)

Question 969507: Please help me solve this proof!
Premises:
1. (A⊃B)&(C⊃D)
2. (E⊃F)&(G⊃H)
3. A&E
Conclusion: BvG

Click here to see answer by Edwin McCravy(20055)

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