Questions on Logic: Proofs answered by real tutors!

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Question 1118662: Still having issues on proofs
1.(A⊃S)⊃G
2. A⊃Q
3. G⊃B
4. Q⊃S / B&G
Click here to see answer by t0hierry(194)

Question 1118661: Trying to write the proof and am stuck.
1.H > J
2.~(J & H) / ~H
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Question 1118993: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.
1. A ⊃ (B ⊃ D)
2. A ⊃ (C ⊃ F) / A ⊃ [(B ⊃ D) � (C ⊃ F)]
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Question 1119188: Use conditional proof or indirect proof to establish the truth of the following tautology.
[~S v ~(~T � ~U)] ⊃ [~U ⊃ (~T ⊃ ~S)]
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Question 1119185: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.
1. R v ~S
2. ~R v T
3. T ⊃ (S � U) / S ≡ T
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Question 1119897: Premises:
1. X ⊃ ~W
2. ~V ⊃ W
Prove: X ⊃ V
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Question 1119896: Premises:
1. A ⊃ X
2. X ⊃ (B ⊃ C)
Prove: (A � B) ⊃ C
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Question 1120001: 1. T ⊃ B Prove: L � B (Hint this involves using the Addition Rule)
2. T ⊃ ~X
3. T
4. X

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Question 1120003: Ana and Beth do a job together in three hours. Working alone, Ana does the job in 5 hours. How long will it take Beth to do the job alone?
A.3 and 1/3 hours
B.2 and 1/3 hours
C. 3 hours
D. 7 and 1/2 hours
Click here to see answer by Shin123(626)

Question 1120553: Could you please help me? Im sick with a bug and cant think straight :/
A)
1. A ⊃ B
2. A ∙ C / B
3.
4.
B)
1. W ⊃ X
2. X ⊃ Y
3. Y ⊃ Z / W ⊃ Z
4.
5.
C)
1. M ⊃ N
2. O ⊃ P
3. M ∨ O / (N ∨ P) ∨ O
4.
5.
6.
D)
1. A ⊃ (R ∙ T)
2. (R ∨ T) ⊃ J
3. A / J
4.
5.
6.
7.
E)
1. (C ⊃ D) � (D ⊃ B)
2. (B ⊃ D) � (E ⊃ C)
3. (D ⊃ C)
4. B ∨ E /D ∨ B
5.
6.
7.
8.
9.
F)
1. (~ K � ~N) ⊃ [(~P ⊃ K) ∙ (~R ⊃ G)]
2. K ⊃ N
3. ~N ∙ B
4. ~P ∨ ~R / ~R ∨ G
5.
6.
7.
8.
9.
10.
11.
12.

Click here to see answer by solver91311(24713)

Question 1125684: Choose one of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the argument. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8.
(G � P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G � ~L) → K
(S v T) ↔ ~E, S → (F � ~G), A → W, T → ~W, therefore, (~E � A) → ~G
(S v T) v (U v W), therefore, (U v T) v (S v W)
~Q → (L → F), Q → ~A, F → B, L, therefore, ~A v B
~S → (F → L), F → (L → P), therefore, ~S → (F → P)

Click here to see answer by jim_thompson5910(35256)

Question 1126460: Below are basic arguments in English. Choose one argument and translate the argument into the symbolism of predicate logic. Use one of the proof techniques from Chapter 8 to demonstrate the validity of the argument.
1.Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul, Rx = x has a right to life).
2.Some wars are just. No war of aggression is just. Therefore, there are wars that are not wars of aggression. (Wx = x is a war, Jx = x is just, Ax = x is a war of aggression).
3.At least one instance of intentional killing is not wrong. But every murder is wrong. Hence, some instances of intentional killing are not murder. (Kx = x is an instance of intentional killing, Wx = x is wrong, Mx = x is murder)
4.Only things that have human bodies are human. No soul has a human body. Only souls survive the death of the body. Therefore, no humans survive the death of the body. (Bx = x has a human body, Hx = x is human, Sx = x is a soul, Dx = x survives the death of the body)

Click here to see answer by Alan3354(69443)

Question 1126462: Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul,

Rx = x has a right to life).(x)(Fx →Sx), (x)(Rx →Sx)∴ (x)(Fx→Rx)
1. (x)(Fx→ Sx) premise
2. (x)(Rx→ Sx) premise ∴ (x)(Fx→ Rx) conclusion
3. Fa Assume(forCP)
4. Fa→ Sa1, UO
5. Ra→ Sa2, UO
6. Sa →Ra 5, CN
7. Fa →Ra 4, 6 CH
let me know if i did it correctly and if and correction need to be made
Click here to see answer by Alan3354(69443)

Question 1126615: Prove by direct proof. (use rules of interference)
1. ~ A -> (C /\ D)
2. A -> B
3. ~B
Prove: C.
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Question 1129033: 1)A>B
2)A/B
Click here to see answer by ikleyn(52778)

Question 1129426: construct a formal proof of validity for the following argument.
1. (M ⊃ N) ● (O ⊃ P)

2. ~ N v ~ P

3. ~ (M ● O) ⊃ Q

4. ∴ Q
Click here to see answer by Edwin McCravy(20054)

Question 1129466: Use Indirect Proof and the 8 Rules of Implication and the 10 Rules of
Replacement of Natural Deduction to derive the stated conclusion from the
given premises:
1. Sv(T�R)
2. S→T /T
Click here to see answer by Edwin McCravy(20054)

Question 1129934: Which is larger or ?
Show conclusions! No calculator.
Click here to see answer by ikleyn(52778)

Question 1129935: Show every step. This is a proof.
If , show that
Click here to see answer by greenestamps(13198)

Question 1130042: Show every step. This is a proof!
If , show that
Click here to see answer by MathLover1(20849)

Question 1130715: (H ∨ M) ∨ L
L ⊃ H
H ⊃ (M ⊃ H)
∼(M ⊃ H) /M
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Question 1130716: (M ∨ R) ⊃ ∼K
(G ⊃ ∼K) ⊃ C
G ⊃ (M ∨ R) /C
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Question 1131132: 1. (A∨G)→K
2. K→(B→F)
3. A∙B
Continue the proof
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Question 1131282: 1. P->~M
2. C->M
3. ~LvC
4. (~P->~E)&(~E->~C)
5. Pv~P /~L

Click here to see answer by Edwin McCravy(20054)

Question 1132066: Prove that the product of two consecutive nonzero even integers is never a perfect square.
NOTE: Please use proof by CONTRADICTION!!
Click here to see answer by Alan3354(69443)

Question 1131581: (A&B)->C
B&~C/ ~A (indirect proof)
Click here to see answer by Edwin McCravy(20054)

Question 1131580: 1.(A&B)⊃C
2. B& ~c/ ~A
(indirect proof
Click here to see answer by Edwin McCravy(20054)

Question 1132243: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.
1. R v ~S
2. ~R v T
3. T ⊃ (S • U)
Conclusion: S ≡ T
Click here to see answer by jim_thompson5910(35256)

Question 1132258: Use conditional proof to derive the conclusion of the following argument.

a) (N v D) ⊃ (M v C)
b) (M v Q) ⊃ C

Conclusion: N ⊃ C
Click here to see answer by jim_thompson5910(35256)

Question 1132257: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.
1. P ⊃ (Q • R)
2. Q

Conclusion: R ⊃ P

Click here to see answer by math_helper(2461)

Question 1132340: solve sin^2 x + 5 (cos(x/2))^2. Thank you.
Click here to see answer by greenestamps(13198)

Question 1132701: 1. ~X>(~Y>Z)
2. Y>X
3. ~Z
conclusion: X
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Question 1132615: 1. A > (B>D)
2. A> (C>F) / A> [(B>D) * (C>F)]
Click here to see answer by Edwin McCravy(20054)

Question 1134211: the grades of javed in nine monthly tests were 58,80is?,56,64,80,56,90,80. the mode of his grades
Click here to see answer by ikleyn(52778)

Question 1134392: a ladder is resting against a vertical wall its base is 1.50m from the base of the wall. when giani steps on the ladder, it falls 0.25m and its base is now 2m away from the wall. find the length of the ladder using pythagoras theorem.

Click here to see answer by josgarithmetic(39617)

Question 1135667: suppose that q is a rational number that is not 0 or 1, and that x is irrational and nonzero. prove that cubic root ((q^2-1)/(qx)) is irrational.
please prove by contradiction (assuming cubic root ((q^2-1)/(qx)) is rational.)
thanks for helping
Click here to see answer by ikleyn(52778)

Question 1135774: Please help! I can't for the life of me figure this one out!
Proof by natural deduction- Predicate Logic. Use a direct proof to show that the following argument is valid.
Premise 1: (∃x)Kx --> (x) (Lx --> Mx)
Premise 2: Kc • Lc
Conclusion: Mc

Click here to see answer by MathLover1(20849)

Question 1137115: Please help me answer this. Thank you in advance
I. Construct formal proof of validity for the following statements:
G.
1. S > U
2. U > (T > V)
3. ~ (T > V) /: . ~S
Click here to see answer by Edwin McCravy(20054)

Question 1137127: how to solve this using the implication rules and replacement rules.
~(SvQ) /~P>~S

Click here to see answer by Edwin McCravy(20054)

Question 1138740: Chef Craig can decorate a dozen cupcakes in half the time of Chef Charlotte. Together they can decorate the dozen cupcakes in 8 minutes. How long would it take each chef to decorate a dozen cupcakes alone?
Click here to see answer by greenestamps(13198)

Question 1138739: In order to create tunnels, civil engineers devise plans where tunnel-boring machines begin drilling at both ends of the tunnel and meet somewhere in between. A tunnel is being built through a section of mountain. One tunnel-boring machine alone can finish the tunnel in 4 years. Another machine can finish the job in 3 years. If both machines start at opposite ends and work at the same time, when will the tunnel be finished?
Click here to see answer by ikleyn(52778)

Question 1139330: A → (B → C) ├ (B & A) → C
Click here to see answer by ichudov(507)

Question 1139524: Is the following argument valid or invalid?
(P) A ⊃ (B • C)
(P) (B v D) ⊃ E
(C) A ⊃ E
Click here to see answer by math_helper(2461)

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