Questions on Logic: Proofs answered by real tutors!

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Question 1171045: Create a poof for the following argument
1. (L ∨ B) ⊃ C
2. (S ∨ D) • L / C
Click here to see answer by math_helper(2461)

Question 1171296: Construct a proof for the following:
1. ~C
2. (~A * B) v (~A * C). .·. B
Click here to see answer by Edwin McCravy(20054)

Question 1171295: Construct a proof for the following:
1. ~(J * L)
2. (J --> ~L) --> (~M * ~X)
3. E v (M v X). .·. E
Click here to see answer by Edwin McCravy(20054)

Question 1171292: Prove the following:
1. O --> (H * M)
2. (O --> G) --> (H --> ~M)
3. ~G --> (~H v ~M) .·. H --> ~M

Click here to see answer by Edwin McCravy(20054)

Question 1171728: 1. J => (L v T) Basic Assumption
2. ~ (L v ~ J) Basic Assumption / ~ L => T

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Question 1171730: 1. (E & I) v (M & U) Basic Assumption
2. ~ E Basic Assumption / ~ M => ~ U

Click here to see answer by Solver92311(821)

Question 1171801: I am trying to use indirect proof to derive the conclusion but I am confused on the steps to get to ~A.
1. (A & B) ⊃C
2. B & ~C/~A

Click here to see answer by Edwin McCravy(20054)

Question 1171806: 1. W ⊃ (P v C)
2. ~P
3. W/C
I am trying to see how they were able to get the conclusion "C"
I think it should be
4. C modus ponens 1,2
But I am not sure if that is correct or if i am on the wrong path.
Click here to see answer by math_tutor2020(3816)

Question 1171807: 1. (J v F) v M
2. (J v M) ⊃ ~ P
3. ~F/~(F v P)
4. M Assumption for Indirect Proof
5.

12. ~(F v P)
I think there are 12 lines to get to the conclusion?

Click here to see answer by math_tutor2020(3816)

Question 1171842: 1. T ⊃ O
2. R v ~O
3. ~R/~T
4. ~T DS 2,3
I think I completed this correctly but I may be missing a step
Click here to see answer by Edwin McCravy(20054)

Question 1171839: [(P ⊃ Q) & P] ⊃ Q
I need to use premise free proof to prove the equation above but I am at a lost on where to start
Click here to see answer by Edwin McCravy(20054)

Question 1171838: 1. A v B
2. A ≡ (C & D)
3. B ⊃ (D & G)/D
I know I need to use indirect proof to derive the conclusion but I am thrown off by the ≡ symbol as we rarely have used that symbol
Click here to see answer by Edwin McCravy(20054)

Question 1171851: 1. (Q ⊃~J) ⊃ (M ⊃~D)
2. Q ⊃M
3. M ⊃ ~J/Q ⊃ ~D
I am at a complete lost with this one. I believe we are gong to use motus ponens and possibly MT as well

Click here to see answer by math_tutor2020(3816)

Question 1171852: 1. T ⊃ (Q & F)
2. T & C/Q v O
I am trying to solve this equation using the inference rules and replacement rules.
I don't think an indirect proof is needed to derive the conclusion
Click here to see answer by math_tutor2020(3816)

Question 1171859: 1. F ⊃ ~U
2. ~F ⊃ P
3. F v ~F/~U v P
I think what is throwing me off with this equation is the use of the two F's in line 3.

Click here to see answer by math_tutor2020(3816)

Question 1171795: Use the inference rules, replacement rules, indirect proof, or conditional proof to derive the conclusion.
1. (Q ⊃ ~J) ⊃ (M ⊃ ~D)
2. Q ⊃ M
3. M ⊃ ~J/Q ⊃ ~D
I am at a complete lost with this equation

Click here to see answer by Edwin McCravy(20054)

Question 1171858: 1) (Q ⊃~J) ⊃ (M ⊃~D)
2) Q ⊃M
3) M ⊃ ~J/Q ⊃ ~D
I am trying to figure out how the conclusion came to be Q ⊃ ~D.

Click here to see answer by math_helper(2461)

Question 1171796: Use a premise-free proof to prove: [(P ⊃ Q) & P] ⊃ Q
Click here to see answer by math_helper(2461)

Question 1171792: 1. A v B
2. A ≡ (C & D)
3. B ⊃ (D & G)/D
I am trying to solve this equation. i do know that I need to use an indirect proof but I am stuck.
Click here to see answer by math_helper(2461)

Question 1171915: If the radius is 5 cm, find the SA and volume of the sphere
Click here to see answer by ikleyn(52775)

Question 1171729: 1. ~ A v ~ S Basic Assumption
2. ~ ~ S Basic Assumption
3. (A => ~ O) & (~ O => A) Basic Assumption
4. (~ O => ~ S) v A Basic Assumption / A => ~ S

Click here to see answer by mccravyedwin(406)

Question 1171802: use the inference rules, replacement rules, indirect proof and/or conditional proof to derive the conclusion.
1. F ⊃ ~U
2. ~F ⊃ P
3. F v ~F/~U v P

Click here to see answer by Edwin McCravy(20054)

Question 1171800: use the inference rules, replacement rules, indirect proof and/or conditional proof to derive the conclusion.
1. T ⊃ (Q & F)
2. T & C/Q v O

Click here to see answer by mccravyedwin(406)

Question 1171799: Use the inference rules to derive the conclusion
1. T ⊃ O
2. R v ~O
3. ~R/~T

Click here to see answer by Plocharczyk(17)

Question 1171799: Use the inference rules to derive the conclusion
1. T ⊃ O
2. R v ~O
3. ~R/~T

Click here to see answer by Edwin McCravy(20054)

Question 1171798: I need to use proofs to derive the conclusion but I am not sure if I should use MP, or DS
1. (Q ⊃~J) ⊃ (M ⊃~D)
2. Q ⊃M
3. M ⊃ ~J/Q ⊃ ~D

Click here to see answer by Edwin McCravy(20054)

Question 1171793: 1. (J v F) v M
2. (J v M) ⊃ ~P
3. ~F/~(F v P)
I need help tryin to figure out what inference rules to use to solve this problem

Click here to see answer by Solver92311(821)

Question 1171516: Could you please help me with this problem?
A → B, A ⋁ C, B → D, ¬C ⊢ E ⋁ D
I need to construct a formal proof.
Thank you!
Click here to see answer by math_helper(2461)

Question 1171518: For any TFL sentences 𝛼, 𝛽, and 𝛾 such that 𝛼 is a contradiction, 𝛽 is a tautology, and 𝛾 is neither a contradiction nor a tautology, do the following entailments hold:
3.2.1. 𝛼 → 𝛼 ⊨ 𝛽 → (𝛽 → 𝛼)
3.2.2. ¬(𝛽 → 𝛾) ⊨ 𝛾 ↔ 𝛼
Thank you!

Click here to see answer by Edwin McCravy(20054)

Question 1176033: Derive the base-to-height ratio equation from lecture 11:
B/H' = (1-PE/100)d/f
Use similar triangle relationships, starting with G/H' = d/f. Symbol definitions are given in the PPT, the figure will be helpful.
Click here to see answer by math_helper(2461)

Question 1176890: Proof by induction. Imagine that we are going to prove by induction that:
(1/sqrt(1)) + (1/sqrt(2)) + (1/sqrt(3)) + ... + (1/sqrt(n)) >= sqrt(n), for all n E Z^+
Assume by the inductive step that:
(1/sqrt(1)) + (1/sqrt(2)) + (1/sqrt(3)) + ... + (1/sqrt(k)) >= sqrt(k), for some k E Z^+
Which of the following is a correct way of ending this proof?
a. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k)) >= sqrt(k) + (1/sqrt(k+1)) = sqrt(k+1) +1 >= sqrt(k+1)
b. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k)) >= sqrt(k+1) + (1/sqrt(k+1)) + (1/sqrt(k+1)) >= sqrt(k+1)
c. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k+1)) >= sqrt(k) + (1/sqrt(k+1)) = (sqrt(k)sqrt(k+1)+1)/sqrt(k+1)) >= (sqrt(k)sqrt(k)+1)/sqrt(k+1)) >= ((k+1)/sqrt(k+1)) = sqrt(k+1)
d. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k+1)) >= sqrt(k) + (1/sqrt(k)) = ((sqrt(k)sqrt(k+1))/sqrt(k)) >= ((k+1)/(sqrt(k+1))) = sqrt(k+1)
Click here to see answer by ikleyn(52775)

Question 1176891: (1/sqrt(1)) + (1/sqrt(2)) + (1/sqrt(3)) + ... + (1/sqrt(n)) >= sqrt(n), for all n E Z^+

Assume by the inductive step that:

(1/sqrt(1)) + (1/sqrt(2)) + (1/sqrt(3)) + ... + (1/sqrt(k)) >= sqrt(k), for some k E Z^+

Which of the following is a correct way of ending this proof?

a. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k)) >= sqrt(k) + (1/sqrt(k+1)) = sqrt(k+1) +1 >= sqrt(k+1)

b. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k)) >= sqrt(k+1) + (1/sqrt(k+1)) + (1/sqrt(k+1)) >= sqrt(k+1)

c. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k+1)) >= sqrt(k) + (1/sqrt(k+1)) = (sqrt(k)sqrt(k+1)+1)/sqrt(k+1)) >= (sqrt(k)sqrt(k)+1)/sqrt(k+1)) >= ((k+1)/sqrt(k+1)) = sqrt(k+1)

d. (1/sqrt(1)) + (1/sqrt(2)) + ... + (1/sqrt(k+1)) >= sqrt(k) + (1/sqrt(k)) = ((sqrt(k)sqrt(k+1))/sqrt(k)) >= ((k+1)/(sqrt(k+1))) = sqrt(k+1)
Click here to see answer by ikleyn(52775)

Question 1177235: Conditional proof
M->(K->L)
(L\/N) -> J
Therefore, M-> (K->J)
That's supposed to be a downward arrow between L and N in the second line
Click here to see answer by math_helper(2461)

Question 1177233: (O->R) -> S
(P->R) ~S
Therefore, ~R
Click here to see answer by Solver92311(821)

Question 1178037: 1.In a certain class of 40 students,28 were listed as an exercise book reader, and 16 as book reader while 8 were listed as exercise book and book readers. Then find out how many students read neither exercise book nor book.
Click here to see answer by ikleyn(52775)

Question 1178231: Prove or disprove: There exists an integer a for which 20a ≡ 2 mod 8.
Click here to see answer by ikleyn(52775)

Question 1178624: Use Indirect proof to solve the following:
B ≡ (A • D)
~A ⊃ (~B ⊃ C) / A ∨ C
Click here to see answer by Edwin McCravy(20054)

Question 1179155: Prove that there exists some integer n such that n^2 + 123457 is a perfect square.
Click here to see answer by Edwin McCravy(20054)

Question 1179120: 1. ~(K v F)
2. ~F ⊃ (K v C)
3. (G v C) ⊃ ~H / ~(K v H)
Click here to see answer by Edwin McCravy(20054)

Question 1179159: Let A = {n C Z | n is odd} and B = {n C Z | n^2 - 1 mod 4}. Prove that A is included in B.
Click here to see answer by ikleyn(52775)

Question 1179180: Question 1
1. ~(U v R)
2. (~R v N) ⊃ (P * H)
3. Q ⊃ ~H ~Q
Question 2
1. (P v U) ⊃ ~L
2. (I v W) ⊃ ~K
3. L • K / ~(U v W)
Question 3
1. R ⊃ (C v M)
2 ~(I v C)
3. ~(A v M) / ~R
could you possibly explain how you got the answer??
Click here to see answer by Edwin McCravy(20054)

Question 1179186: 1. ~(U v R)
2. (~R v N) ⊃ (P * H)
3. Q ⊃ ~H / ~Q
Click here to see answer by math_helper(2461)

Question 1178950: Use the first five rules of replacement (DM,Com, Assoc, Dist, DN) together with the eight rules of implication to prove this argument is valid.
1. H ⊃ ~A
2. A /~(H v ~A)

Click here to see answer by Edwin McCravy(20054)

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