Questions on Logic: Proofs answered by real tutors!

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Question 1179403: The position of an object at Time t is given by s(t)=-1-13. Find the instantaneous velocity at t=8 by finding the derivative
Click here to see answer by ikleyn(52777)

Question 1179550: Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.
(iA: inverse of A).
Click here to see answer by ikleyn(52777)

Question 1179552: Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.
(iA: inverse of A).
Click here to see answer by ikleyn(52777)

Question 1179560:
1. ~X ⊃ ~~O
2. ~X ⊃ A
3. ~(O * A) / X
Click here to see answer by Edwin McCravy(20054)

Question 1179783: A water heater consumed 18 kWh of electrical energy when it is used for 15 minutes per day for one month. Calculate the electrical power of the water heater. Assume 30 days in one month. ( Include units and if necessary round to 1 decimal place)
Click here to see answer by ikleyn(52777)

Question 1179981: Use Indirect Proof to solve the following argument.
1. (C v R) ⊃ (N • I)
2. (N v P) ⊃ (I ⊃ ~C) /~C
Click here to see answer by Edwin McCravy(20054)

Question 1179976: 1. O ⊃ (Q • N)

2. (N ∨ E)⊃ S / O ⊃ S

Click here to see answer by Edwin McCravy(20054)

Question 1180012: Select the conclusion that follows in a single step from the given premises.
1. ~(G • H)
2. ~F > H
3. (G > ~F) • (~F > G)
Click here to see answer by Edwin McCravy(20054)

Question 1179973: Use an ordinary proof (not conditional or indirect) to solve the following arguments.
1. (O ⊃ R) ⊃ S
2. (P ⊃ R) ⊃ ~S/ ~R
Click here to see answer by Edwin McCravy(20054)

Question 1179971: Use an ordinary proof (not conditional or indirect) to solve the following arguments
1. P ⊃ ~M
2. C ⊃ M
3. ~L v C
4. (~P ⊃ ~E) • (~E ⊃ ~C)
5. P v ~P /~L
Click here to see answer by Edwin McCravy(20054)

Question 1179975: 1. P ⊃ ~M
2. C ⊃ M
3. ~L v C
4. (~P ⊃ ~E) • (~E ⊃ ~C)
5. P v ~P /~L
Click here to see answer by Solver92311(821)

Question 1181005: How would I finish this conditional proof?
Practice for an upcoming exam
1. (B ⊃ ∼M) ⊃ (T ⊃ ∼S)
2. B ⊃ K
3. K ⊃ ∼M
4. ∼S ⊃ N ∴ T ⊃ N - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Click here to see answer by math_helper(2461)

Question 1181578: Let p, q, r and s represent the following: Determine the truth value of each statement.
P: 2 is the smallest prime number. True
q: The capital city of Camiguin is Mambajao. True
r: The sum of 2 odd numbers is odd. False
s: The diagonals of a parallelogram are congruent. False

Click here to see answer by ikleyn(52777)

Question 1181636: Find the truth value of the following: Show the solution.
4. (q∨r)↔[(¬q→(r∧¬p))]
5. (¬s↔(r→¬q))↔[(s∨p)∧¬(q∧r)]
Click here to see answer by Edwin McCravy(20054)

Question 1183367: prove that n^2 ≤ n! for all n ≥ 4 using mathematical induction
Click here to see answer by ikleyn(52777)

Question 1183367: prove that n^2 ≤ n! for all n ≥ 4 using mathematical induction
Click here to see answer by math_helper(2461)

Question 1183366: prove that n^2 ≤ n! for all n ≥ 4 using mathematical induction
Click here to see answer by ikleyn(52777)

Question 1183377: Translate the following argument into symbolic form (be sure to provide a key) and then
prove that it is valid using natural deduction:
1. If consciousness is physical and the brain is a computer,
Click here to see answer by ikleyn(52777)

Question 1183507: F → (O • B), S ↔ ~B, , W ↔ ~S, therefore F → W
to demonstrate the validity of the argument. Your proof may utilize any of the Rules of Inference or Equivalence Rules given in Chapter 8.
Click here to see answer by math_helper(2461)

Question 1187346: 1. (O ⊃ C ) ● (∼S ⊃ ∼D)
2. (E ⊃ D) ● (∼E ⊃ ∼C ) / O ⊃ S

Click here to see answer by Edwin McCravy(20054)

Question 1187790: P1 (A ∨ B) ⊃ C
P2 (∼A ∨ D) ⊃ E
CONCLUSION C ∨ E

Click here to see answer by math_helper(2461)

Question 1187551: I. Evaluate the following arguments:
1.
1. ∼B ⊃ [(A ⊃ K ) ⊃ (B v ∼K )] 2. ∼J ⊃ K 3. A ⊃ ∼J 4. ∼B /~A
2.
1. (R ⊃ F) ⊃ [(R ⊃ ∼G) ⊃ (S ⊃ Q)] 2. (Q ⊃ F ) ⊃ (R ⊃ Q) 3. ∼G ⊃ F 4. Q ⊃ ∼G / S ⊃ F
II. The following symbolized arguments are missing a premise. Write the premise
needed to derive the conclusion (last line ), and supply the justification for
the conclusion. Try to construct the simplest premise needed to derive the
conclusion.
1.
1. C v L
2. L ⊃ T
3. ______
4. L ____
2.
1. E ⊃ N
2. T v ∼E
3. S ⊃ E
4. ______
5. E ____
3.
1. ∼R ⊃ D 2. ∼J ⊃ ∼R 3. N v ∼R 4. ______
5. ∼F ⊃ ∼R
Click here to see answer by Edwin McCravy(20054)

Question 1187067: A. Tell whether each of the following is a proposition or not. In case of a proposition, indicate if it is true or false. If it is not a proposition tell why?
1. All multiples of 5 are odd numbers.
2. Five is greater than 4
3. The sun is shining.
4. It is raining.
5. Come to class.
6. All perfect squares are even numbers.
7. Every decimal number is a rational number.
8. 3y -5 = 4
9. The sum of two real numbers is a real number.
10. Some Filipinos are hospitable.

Click here to see answer by Boreal(15235)

Question 1188427: Use indirect proof:
1. (P ∨ F) ⊃ (A ∨ D)
2. A ⊃ (M • ∼P)
3. D ⊃ (C • ∼P) / ∼P

Click here to see answer by Edwin McCravy(20054)

Question 1188710: 1. I v (N&F)
2. I > F /F

using rules of inference & replacement

Click here to see answer by Solver92311(821)

Question 1188729: is the argument invalid or valid?
1. R ⊃ (K • U)
2. A ⊃ (Q • R)
3. S • A ∴ U
Click here to see answer by math_tutor2020(3816)

Question 1188628: B ⊃ ∼C
C ∨ [D ∨ (G • K)]
∼G ∨ ∼K
B ⊃ D
Create a method for the following argument using the conditional proof method.
Click here to see answer by mccravyedwin(406)

Question 1188620: 1. A v (B v C)
2. C ⊃ (D • E)
3. ~D / A v B

Click here to see answer by mccravyedwin(406)

Question 1188424: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
(H v K) ⊃ (L v K), M ⊃ [H⊃ (N • ~L)] /.: (M • H) ⊃ (N • K)

Click here to see answer by math_helper(2461)

Question 1188619: 1. ~(~C • D)
2. ~D ⊃ E
3. C ⊃ ~F //F ⊃ E

Click here to see answer by Edwin McCravy(20054)

Question 1188618:
1. A ⊃ B
2. C ⊃ D
3. ~(D v B) // C ≡ A

Click here to see answer by Edwin McCravy(20054)

Question 1188933: (f⊃g) v h/∼ f
∼G
∼H
Click here to see answer by Solver92311(821)

Question 1188426: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
A v (~B v ~C), A ⊃ (D ⊃ E), ~(~B v ~D) /.: C ⊃ E
Click here to see answer by Edwin McCravy(20054)

Question 1188875: Use conditional proof or indirect proof as needed:
1. (x)[Rx⊃(Tx •∼Ex)]
2. (x)[(Qx • Rx)⊃Ex] / (x)(Rx⊃∼Qx)
Click here to see answer by Edwin McCravy(20054)

Question 1188627: R ⊃ ∼U
P ⊃ (Q ∨ R)
(Q ⊃ S) • (S ⊃ T)
P ⊃ (∼U ∨ T)

Click here to see answer by Edwin McCravy(20054)

Question 1188400: 1. P ⊃ [ ( L v M ) ⊃ ( N • O ) ]
2. ( O v T ) ⊃ W / P ⊃ ( M ⊃ W )

Click here to see answer by Edwin McCravy(20054)

Question 1188425: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid:
(A • B) ⊃ (E ⊃ A), (A • B) v C, C ⊃ D /.: (E ⊃ A) v D
Click here to see answer by Edwin McCravy(20054)

Question 1189673: I am having trouble solving this proof.
THEOREM IS ¬S∧¬R ⊢ (¬R∧¬S)→¬(S∨R)
Please let me know if you can figure it out !
Click here to see answer by math_helper(2461)

Question 1190080: 1.(N V O) ⊃ (C • D)
2.(D V K) ⊃ (P V ~C)
3.(P V G) ⊃ (N • D)
∴ ~N
Click here to see answer by math_tutor2020(3816)

Question 1190083: Solve the following by using only the 18 rules of implication
and replacement to get: (H • U) ⊃ (S • D)
1. H ⊃ D
2. U ⊃ S

Click here to see answer by Edwin McCravy(20054)

Question 1190255: Topics In Contemporary Math
Arguments
Use truth tables to determine if each of the following arguments are valid or invalid.
4) If you back up your hard drive, then you are protected.
Either you are protected or you are daring.
Therefore, if you are daring, then you won’t back up your hard drive.
Click here to see answer by math_tutor2020(3816)

Question 1190301: Topics In Contemporary Math
Modus Ponens and Modus Tollens

Translate each of the following into symbols, then determine whether or not the argument
is valid by providing the appropriate name for the argument form.
3) I studied or I failed the class.
I did not fail the class.
Therefore, I studied.
Click here to see answer by math_tutor2020(3816)

Question 1190299: Topics In Contemporary Math
Modus Ponens and Modus Tollens
1) Create a truth table to prove that the Law of Disjunctive Syllogism is a valid argument
form.

Click here to see answer by math_tutor2020(3816)

Question 1190300: Topics In Contemporary Math
Modus Ponens and Modus Tollens
Another invalid argument form is the Fallacy of the Inclusive “or”, which has the
argument form
𝑝 𝑉 𝑞
𝑝
∴ ~𝑞
Create a truth table to prove that this argument form is invalid.
Translate each of the following into symbols, then determine whether or not the argument
is valid by providing the appropriate name for the argument form.
Click here to see answer by math_tutor2020(3816)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485