Questions on Logic: Proofs answered by real tutors!

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Question 1023500: Determine whether a statement
n^2 + n + 401
is prime for every natural n is true or false. State and prove a theorem based on this statement.

Click here to see answer by ikleyn(52775)

Question 1023504: Prove that
1^2 + 3^2 + . . . + (2n − 1)^2 =1/3(4n^3 − n)
for all natural numbers n.
Click here to see answer by robertb(5830)

Question 1024363: Prove the following three arguments to be valid using the method of Natural Deduction
A. 1. ~(S v E)
2. [(O v M) -> S] / ~M
B. 1. [Q v (K v R)]
2. (~W & ~R) / (K v Q)

C. 1. [(L v P) -> U]
2. [(M -> U) -> I
3. ~(P -> B) / I

Click here to see answer by solver91311(24713)

Question 1025356: Please help me solve this Indirect Proof Equation
1.) (B&C)>[R>(S&T)]
2.) (CvD)>(R&~S)
3. B>C ................. /~B
(What I have so far?)
4. B ............. AIP
5. B&C ..........4, Com
6. R>(S&T).....1,5 MP
Click here to see answer by Edwin McCravy(20054)

Question 1025707:
1. (AvB) ⊃ C 2. (CvD) ⊃ (EvF) 3. A●~E / F

Click here to see answer by Edwin McCravy(20054)

Question 1026080: 1. ~ ( H v ~K )
2. L --> H / L --> M

Click here to see answer by Edwin McCravy(20054)

Question 1026581: 1. A -> ~(B v C)
2. ~D -> (~A -> ~E)
3. ~(~E v F)
4. ~F -> (A -> B) /D
I don't understand how to do this proof with the
conclusion being "D".
Click here to see answer by Edwin McCravy(20054)

Question 1026724: Please help me complete the conditional proof for this problem:
(F v ~ G) → ~ L .: L → G
Click here to see answer by jim_thompson5910(35256)

Question 1026781: I am trying to solve this proof:
premises: A or B, A or C
goal: A or (B and C)
I know that I need to use subproofs to solve this, but I don't know how far I need to break down each premise with a subproof to solve this.

Click here to see answer by richard1234(7193)

Question 1028017: I'm having a hard time constructing a proof for the following argument.
M&~Q
M->S
S->P
And the goal is ~(P->Q)
Click here to see answer by richard1234(7193)

Question 1028017: I'm having a hard time constructing a proof for the following argument.
M&~Q
M->S
S->P
And the goal is ~(P->Q)
Click here to see answer by Edwin McCravy(20054)

Question 1028160: 1. A > B
2. C > D
3. K > (A v C)
4. J v K
5. J > Z
6. W & ~Z / B v D
Click here to see answer by jim_thompson5910(35256)

Question 1028652: Natural Deduction
How do I solve the proof:
1. (Av~B)⊃((A�C)⊃B)
2. ~B /A⊃~C
Click here to see answer by Edwin McCravy(20054)

Question 1029122: COMPLETE THE FOLLOWING PROOFS USING CONDITIONAL PROOF
Premises:
1. Y ⊃ ( N � U)
2. S ⊃ (~N � U)
Conclusion:
/ Y ⊃ ~S
Click here to see answer by robertb(5830)

Question 1029123: COMPLETE THE FOLLOWING PROOFS USING CONDITIONAL PROOF
Premises:
1. G ⊃ (E ⊃ N)
2. H ⊃ (~N ⊃ E)
Conclusion:
G ⊃ ( H ⊃ N)

Click here to see answer by robertb(5830)

Question 1029119: COMPLETE THE FOLLOWING PROOFS WITHOUT USING CONDITIONAL PROOF OR
INDIRECT PROOF
Premises:
1. T ∨ (P ∨ S)
2. ~T
3. P ⊃ Q
4. ~T ⊃ (S ⊃ L)
Conclusion: Q V L
Click here to see answer by robertb(5830)

Question 1029291: Hi! I really could use some help solving these two proofs below. I also included instructions!
Instructions: You must construct a proof for two of the following. All proofs include at least 4 steps (besides the original premises).
I have left the section and problem numbers so that you can check your answers online before posting them. Here is the website for checking your answers:
http://www.poweroflogic.com/cgi/menu.cgi
You can expand the readable area to show the whole argument by clicking and dragging on the triangle shape at the bottom right of this area.
Questions from The Power of Logic 5th Edition/Chapter 8/Section 8.3/Part C
15. (~D v E) � (~D v ~F), (E � ~F) → ~G, ~D → ~G ∴ ~G
24. ~O ∴ ~Q → ~(O � P)
Please & Thank you :)
Click here to see answer by jim_thompson5910(35256)

Question 1029344: COMPLETE THE FOLLOWING PROOFS WITHOUT USING CONDITIONAL PROOF OR
INDIRECT PROOF (10 PTS. EACH)
PROOF 1:
1. A
2. B / A ≡ B

Click here to see answer by Edwin McCravy(20054)

Question 1029581: Please complete the following natural deduction proof.
1. A ⊃ U
/ A ⊃ (K ⊃ U)

Click here to see answer by robertb(5830)

Question 1029579: Complete the following natural deduction proof. Thank you!
1. (R � J) ⊃ U
2. ~(~R � ~N)
3. J
/ U v N

Click here to see answer by robertb(5830)

Question 1029805: Please solve using natural deduction (only rules of implication + rules of replacement). Thx!
1. A ⊃ U
/ A ⊃ (K ⊃ U)

Click here to see answer by Edwin McCravy(20054)

Question 1029802: Use an ordinary proof to show the conclusion can be derived from the premises.
1. K ⊃ L
2. ~K v F
3.(L � F) ⊃ A
4. ~A /~K
Click here to see answer by Edwin McCravy(20054)

Question 1029890: Use an ordinary proof to show the conclusion can be derived from the premises.
1. ~N ⊃ (~R ⊃ C)
2. R ⊃ N
3. ~C / N

Click here to see answer by robertb(5830)

Question 1030073: Use an ordinary proof to show the conclusion can be derived from the premises.
1. G ⊃ (H ⊃ K)
2. (H v ~M) ⊃ ~K
3. H /~G
Click here to see answer by Edwin McCravy(20054)

Question 1029804: Solve the following proof using natural deduction (rules of replacement and rules of implication).
1. D v Y
2. Y ⊃ ~(Z ⊃ D)
/ Y ≡ ~D

Click here to see answer by robertb(5830)

Question 1030232: Help me solve the following using an indirect proof. I am including what I have so far.
1.(AvB)>(C&D)
2.(CvE)>~B
3.(DvF)>~A / ~A&~B
4.~(~A&~B) AIP
5.~~Av~~B 4,DM
6.C&D 1,5 MP
7.C 6, Simp

Click here to see answer by jim_thompson5910(35256)

Question 1030684: I have to construct a proof in propositional logic.
1.(Z>C) � A
2. D v (C>D)
3. ~ D /~ZvP
The > represents the horseshoe meaning if then, only if.
Click here to see answer by Edwin McCravy(20054)

Question 1031108: Q & P, R & -T / -T & Q

Click here to see answer by solver91311(24713)

Question 1031285:
Given the following premises:

1. (~H � ~J) > K
2. ~(~H � ~J)
3. (~H � N) v (~H � ~J)

What would be the conclusion that would result from a single step?

Click here to see answer by Edwin McCravy(20054)

Question 1031401: ∼A∙~B
~D⊃A
M⊃[(NvO)⊃P]
Q⊃(SvT)
(~Qv~R)⊃(M∙N)
~Dv~(SvT) ∴P∙~B
Click here to see answer by jim_thompson5910(35256)

Question 1031400: ∼S⊃(N⊃T)
~S∙(R⊃S)
(~M∙~N)⊃(~Ov~P)
(Qv~R)⊃~M
(~R∙~S)⊃(~~O∙~T) /~P
Click here to see answer by solver91311(24713)

Question 1031311: 1. ∀x(~(Fx v Gx) -> Hx)
2. ∀x(Hx -> Lx)
3. ∀x(~Fx) Conclusion: ∀x(Gx v Lx)
Could you solve this using the quantifier rules, identity rules, eight rules of inference and ten equivalence rules please?
Click here to see answer by robertb(5830)

Question 1031927: Can you please help me complete the following rules by adding the implication rules to each line! Please & Thank you!!!!!!!! Will give u an amazing review :)
Problem #1: ~ A v (B � C), ~ (~ B � A) → ~ C .: ~ A
1. ~ A v (B � C)
2. ~ (~ B � A) → ~ C .: ~ A
3. (~ A v B) � (~ A v C)
4. ~ A v B
5. ~ A v ~ ~ B
6. ~ (A � ~ B)
7. ~ (~ B � A)
8. ~ C
9. ~ A v C
10. ~ A
Problem #2: (M � N) → O, ~ M ↔ ~ L .: L → (N → O)
1. (M � N) → O
2. ~ M ↔ ~ L .: L → (N → O)
3. M → (N → O)
4. (~ M → ~ L) � (~ L → ~ M)
5. ~ M → ~ L
6. L → M
7. L → (N → O)

Click here to see answer by robertb(5830)

Question 1032209: how to solve this logic proof
(1)(I&E)>~F
(2)Fv(G&H)
(3)I=E /(conclusion) I>G
(Key: "&"= and, ">"= if_then_, "~"= not, "v"= or, "="= if and only if
Click here to see answer by robertb(5830)

Question 1032740: If there is not an afterlife, then all is hopeless. If all is hopeless, despair is the right attitude. Despair is not the right attitude. Therefore, there is an afterlife. (A, H, D)
Click here to see answer by addingup(3677)

Question 1032774: 1. (I&E) ⊃ ~F 2. F∨(G & H) 3. I≡E/ I⊃G
Click here to see answer by Edwin McCravy(20054)

Question 1033348: Hello. We have been working on formal proofs in class and this one seems to be difficult for me. I have been having a hard time.
1. (A>~R)>W
2. ~(A+R) :. W v ~R
I don't even know where to start. Thank you for your help.
Click here to see answer by jim_thompson5910(35256)

Question 1033385: hello, I had trouble with this other question as well. It looks simple but I have tried many ways of doing this and I cant figure it out. thank you.
1. S>~G
2. ~(E*~S) :. E>~G
Click here to see answer by robertb(5830)

Question 1033317: (A>~R)>W
~(A*R) .: W v ~ R
Click here to see answer by robertb(5830)

Question 1033666: Knowing that Sqrt(2) is not a rational number, prove that 1-(1/Sqrt(2)) is not a rational number.
Click here to see answer by robertb(5830)

Question 1033666: Knowing that Sqrt(2) is not a rational number, prove that 1-(1/Sqrt(2)) is not a rational number.
Click here to see answer by ikleyn(52775)

Question 1033709: I have no idea what do with this one help please
INSTRUCTIONS: Construct a regular proof to derive the conclusion of the following argument:
1. H v (~T > R)
2. Hv (E > F)
3. ~T v E
4. ~H & D / R v F
Click here to see answer by robertb(5830)

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