Questions on Logic: Proofs answered by real tutors!

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Question 1193810: Prove directly - NO Conditional Proof or Indirect Proof.
1. R ⊃ A / R ⊃ ( A v W )
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Question 1193969: What are the proof steps for A ≡ (B ≡ C) // (A ≡ B) ≡ C ?
Click here to see answer by Edwin McCravy(20054)

Question 1195207: Show that for any integer n,5 | (n^5-n).

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Question 1195208: Prove that
|n/2|*|n/2| = |(n^2)/4|
For all integers 𝑛.

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Question 1195752: 3. [10] Fill in the derived statements
1. R
2. K ⊃ (~X • ~R)
3. (J v Z) v K / ∴ Z v J
4. _____________________ 1 DI
5. _____________________ 4 DeM
6. _____________________ 5, 2 MT
7. _____________________ 6, 3 DS
8. _____________________ 7 comm
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Question 1195751: Phil 10
4. [10] use only inference and replacement rules (no CP or IP):
1. (~P v ~R) v ~S / ∴ P ⊃ ~(S • R)
Click here to see answer by Edwin McCravy(20054)

Question 1195751: Phil 10
4. [10] use only inference and replacement rules (no CP or IP):
1. (~P v ~R) v ~S / ∴ P ⊃ ~(S • R)
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Question 1195750: phil 10
[10] Use indirect proof:
/ ∴ ~~{[Z v (Z ⊃ Q)] v M}
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Question 1195749: Phil 10
7. [10] Use indirect proof:
/ ∴ P ⊃ P
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Question 1195749: Phil 10
7. [10] Use indirect proof:
/ ∴ P ⊃ P
Click here to see answer by Edwin McCravy(20054)

Question 1196247: (y→z)&(z→y) (∴(y&z)v(~y&~z))
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Question 1198251: 1.S>(R&~T)
2.(S&R)>(TvE)
3.(Qv~T)>~E /~S
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Question 1198250: 1. M>(R&E)
2. (EvH)>G /M>G
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Question 1198762: Use Indirect proof to solve the following:
(P v F) ⊃ (A v D)
A ⊃ (M • ~P)
D ⊃ (C • ~P) / ~P
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Question 1199150: Use direct or indirect truth table method to determine whether the following argument is valid.
S ≡ (N • H) / S v ~N // S ⊃ H
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Question 1199146: 1. G⊃(H⊃K)
2. (H∨∼M)⊃∼K
3. H / ∼G
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Question 1199146: 1. G⊃(H⊃K)
2. (H∨∼M)⊃∼K
3. H / ∼G
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Question 1199148: Use direct or indirect truth table method to determine whether the following argument is valid.
S º (N • H) / S Ú ~N // S É H
Click here to see answer by Edwin McCravy(20054)

Question 1198902: Use natural deduction to prove the following logical truth:
(P ⊃ Q) ≡ [P ⊃ (Q ∨ ∼P)]
Click here to see answer by Edwin McCravy(20054)

Question 1199145: Use one of the 3 methods of syllogistic logic to determine whether the following syllogism is
valid:
No carrots are red fruits.
Some fruits are carrots.
Therefore, some fruits are not red fruits.
Click here to see answer by Edwin McCravy(20054)

Question 1199485: Prove that there is only one pair of (integer) perfect squares that differ by 53, and find it.
Thank you!

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Question 1199779: The Rhind Mathematical Papyrus, an Egyptian document dating from circa 1650 BC, states that the area of a circular field of diameter 9 units is equal to the area of a square with a side of 8 units. This sets the ancient Egyptian value of π (pi) at
a) 3
b) 3 1/8
c) 3 1/9
d) 3 9/64
e) 3 13/81
Click here to see answer by Theo(13342)

Question 1201495: For each of the following lists of premises, derive the indicated conclusion and complete the justification. In problems 4 and 8 you can add any statement you choose.
(1) 1. S ∨ H 2. B • E 3. R ⊃ G 4. _____ ____, Simp
(2) 1. (N ⊃ T) • (F ⊃ Q) 2. (N ⊃ R) ∨ (F ⊃ M) 3. N ∨ F 4. _______________ ____, CD
(3) 1. D 2. W 3. ____ ____, Conj
(4) 1. H 2. ____ ____, Add
(5) 1. R • (N ∨ K) 2. (G • T) ∨ S 3. (Q • C) ⊃ (J • L) 4. _____________ ____, Simp

Click here to see answer by Edwin McCravy(20054)

Question 1201675: Use rules of implication to derive the indicated conclusions.
1. R ⊃ (G v ~A) 2. (G v ~A) ⊃ ~S 3. G ⊃ S 4. R/~A
1. ~N⊃ [(B ⊃ D) ⊃(N v~E)] 2. (B ⊃ E) ⊃ ~N 3. B ⊃ D 4. D ⊃ E / ~D
1. ~M ⊃ Q 2. R ⊃ ~T 3. ~M v R / Q v ~T
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Question 1201683: 1. ~N⊃ [(B ⊃ D) ⊃(N v~E)] 2. (B ⊃ E) ⊃ ~N 3. B ⊃ D 4. D ⊃ E / ~D
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Question 1201731: Eight rules of implication
1. G>(S•T)
2.(SvT)>J
3.G. /J
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Question 1201731: Eight rules of implication
1. G>(S•T)
2.(SvT)>J
3.G. /J
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Question 1201697: Is the rule of conjunction like this example true? P v Q
Q v P
(P v Q) · (Q v P)
Is this example a disjunctive syllogism? P v Q
~Q__
~P

The last question I need help on is this a simplication proof example A v B
A

Click here to see answer by mccravyedwin(406)

Question 1201944: Can You please help me solve these proofs? The first statement I'm using the horseshoe symbol.
1.(~F v X)  (P v T)
F  P
~P // T
2. J v (K · L)
~ K //  J
3. ~ (N · T)
T // ~ N

Click here to see answer by Edwin McCravy(20054)

Question 1202690: Are there any mistakes made in solving the following problem? If so, provide the correct answer.
1. W ⊃ Z
2. Z ⊃ (X ∨ Y)
3. Y • W
4. X ⊃ U
5. Y ⊃ V / U ∨ V
6. W 3, Simp
7. W ⊃ (X ∨ Y) 1, 2, HS
8. X ∨ Y 7, 6, MT
9. U ∨ V 4, 5, CD

Click here to see answer by RBryant(14)

Question 1179974: 1.I v (N • F)
2.I ⊃ F /F
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Question 1156947: 1. (G⊃J) ⊃ (H⊃Q)
2. J • ~Q /~H

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Question 1179970: Use an ordinary proof (not conditional or indirect) to solve the following arguments.
1.I v (N • F)
2.I ⊃ F/F
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Question 1179977: 1. (O ⊃ R) ⊃ S
2. (P ⊃ R) ⊃ ~S / ~R

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Question 1202817: 1. (X v B) ⊃ ~J
2. S ⊃ J
3. X / ~S
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Question 1179972: Use an ordinary proof (not conditional or indirect) to solve the following arguments
1. O ⊃ (Q • N)
2. (N Ú E) ⊃ S/ O ⊃ S
Click here to see answer by RBryant(14)

Question 1179972: Use an ordinary proof (not conditional or indirect) to solve the following arguments
1. O ⊃ (Q • N)
2. (N Ú E) ⊃ S/ O ⊃ S
Click here to see answer by Edwin McCravy(20054)

Question 1179972: Use an ordinary proof (not conditional or indirect) to solve the following arguments
1. O ⊃ (Q • N)
2. (N Ú E) ⊃ S/ O ⊃ S
Click here to see answer by math_tutor2020(3816)

Question 1156255: 1. ~A ⊃ ~B
2. A ⊃ C
3. Z ⊃ W
4. ~C • ~W /∴~B v W

Click here to see answer by RBryant(14)

Question 1188428: Use natural deduction to prove the following logical truth:
// [F • (D ⊃ ∼ F)] ⊃ (D ⊃ A)

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Question 1179871: 1. P (horseshoe) ~M
2. C (horseshoe) M
3. ~L v C
4. (~P (horseshoe) ~E) • (~E (horseshoe) ~C)
5. P v ~P /~L

Click here to see answer by RBryant(14)

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