Questions on Logic: Proofs answered by real tutors!

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Question 847697: Prove or disporove. If (n^3)+2 is odd then n^2 is odd where n is an element of all integers.
Click here to see answer by swincher4391(1107)

Question 847700: Prove the following statement. If a is an element of all integers (Z) then 4 is not a divisor of ((a^2)-7)
Click here to see answer by swincher4391(1107)

Question 850169: A bacteria colony begins with 6 individuals and doubles in size every hour. Write down a recurence for a in n terms, the population at the beginning of hour n, and solve it. How many hours elapse until the population exceeds one million?

Click here to see answer by josgarithmetic(39617)

Question 850395: Use induction to show that 5^n-1 is divisible by 4.
Click here to see answer by FrankM(1040)

Question 856463: How can I prove that for each positive integer n, the sum of the first n odd positive integers is n^2 using induction?
Click here to see answer by tommyt3rd(5050)

Question 857321: Find the following; (1) A INTERSECTION {A}. (2) {A,{A}}-A
Click here to see answer by Edwin McCravy(20055)

Question 867064: Prove This:
1. B∨~C
2. B→E
3. ~~C ∴ ~B∨E
Click here to see answer by jim_thompson5910(35256)

Question 868768: Construct a formal proof for the following argument
1. P>R
2. (Q&P)vP
Conclusion R
Click here to see answer by Edwin McCravy(20055)

Question 869136: 1. (F . M) > (S v T) 2. (~S v A) > F 3. (~S v B) > M 4. ~S . G / T
Click here to see answer by jim_thompson5910(35256)

Question 869283: 1. Av (B&C)
2. G-> (~A&~C) So: L-> ~G
Click here to see answer by jim_thompson5910(35256)

Question 869388: There are 4 shut doors in front of you. You know that each door has an animal painted on one side and a plant painted on the other side. The four doors have the following painted on the sides that you can see (one per door): a lily, a pine tree, a fox, and an eagle. You have been told that these doors satisfy the rule "if a door has a flower on its plant side, then it has a bird on its animal side". What is the smallest set of doors that you must check the hidden side of to determine conclusively whether this rule is true or false for these doors?
a) All the doors
b) Just the door with the lily
c) Just the door with the eagle
d) Just the doors with the lily and the eagle
e) Just the doors with the lily and the fox
f) Just the doors with the lily, fox and eagle
g) Just the doors with the pine tree and eagle

Click here to see answer by richwmiller(17219)

Question 869791: I've been stuck on this one for hours, any help would be super appreciated!
Use an ordinary proof (not conditional or indirect proof):
1. ~N > (~R > C)
2. R > N
3. ~C // N
Click here to see answer by jim_thompson5910(35256)

Question 869909: Given
1. P≡~C
2. ~(P&D)
3. D
Prove C
Click here to see answer by jim_thompson5910(35256)

Question 869967: Alright, I have access to rules:
1.Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Constructive dilemma 6. Simplification 7. conjunction 8. addition 9. demorgan 10. commutative 11. associative 12. Distribute 13. Double negate 14. transposition 15. Implication 16. equivalence 17. exportation 18. tautology
Please help with this:
1. ~(X*Y)>Z
2. Z>Y
conclusion: Y
Click here to see answer by jim_thompson5910(35256)

Question 869969: Alright, I have access to rules:
1.Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Constructive dilemma 6. Simplification 7. conjunction 8. addition 9. demorgan 10. commutative 11. associative 12. Distribute 13. Double negate 14. transposition 15. Implication 16. equivalence 17. exportation 18. tautology
Please help with this:
v=or
1. D v C
2. C > (F v D)
3. ~F
conclusion: D
Click here to see answer by jim_thompson5910(35256)

Question 870310: Alright, I have access to rules:
1.Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Constructive dilemma 6. Simplification 7. conjunction 8. addition 9. demorgan 10. commutative 11. associative 12. Distribute 13. Double negate 14. transposition 15. Implication 16. equivalence 17. exportation 18. tautology
You may also use Indirect or conditional proof on this..
Please help with this:
1. (Z * M) > (S v A)
2. Z > ~S
Click here to see answer by Wolfae(1)

Question 870562: 1.M<->N
2.~Mv~N
3.O>M
/~(NvO)
Click here to see answer by jim_thompson5910(35256)

Question 735290: 1. (P>K) V (F>Y)
2. (PvF) . (KvY)
3. [(P>K)>~N]. [(F>Y)>O]
4. K . ~Y
/ ~NvO

Click here to see answer by jim_thompson5910(35256)

Question 737908: 1. K > ~K
2. (~S v U)> K
/ S
Click here to see answer by jim_thompson5910(35256)

Question 531393: hey can you help me with these proofs?
1. ~(J & K) prem
2. ~(L & M) prem
3. J v L / ~(K & M) prem/conc
4.
5.
6.
7.
8.

1.~ P v Q prem
2.~ R > ~Q prem
3.~(R & ~S) / P > S prem / conc
4.
5.
6.
7.
8.
Click here to see answer by jim_thompson5910(35256)

Question 871022: Please help me create this proof using the 18 rules of inference. I have been working on this for hours.
1. (P ∨ F) ⊃ (A ∨ D)
2. A ⊃ (M � ~P)
3. D ⊃ (C � ~P)
∴~P

Click here to see answer by jim_thompson5910(35256)

Question 293877: Use an ordinary proof to solve
1) 1.E ⊃ (S ⊃ T)
2.(~L ⋅ M)⊃(S ⋅ E)
3.~ (T v L) /~M
Click here to see answer by jim_thompson5910(35256)

Question 293878: Use an ordinary proof to solve
1) 1.E ⊃ (S ⊃ T)
2.(~L ⋅ M)⊃(S ⋅ E)
3.~ (T v L) /~M
Click here to see answer by jim_thompson5910(35256)

Question 878323: how is 6+7=9
Click here to see answer by AnlytcPhil(1806)

Question 879828: Prove the product of an integer and its square is even.
Click here to see answer by jim_thompson5910(35256)

Question 881255: Premise 1: D⊃ [D⊃ (B & ~Q)]
Premise 2: (~Q & B)⊃ C
Conclusion: D⊃ C
Direct Deduction
Click here to see answer by jim_thompson5910(35256)

Question 882094: Prove the following identity: cos(x-y)/cosxcosy=1+tanxtany
Click here to see answer by lwsshak3(11628)

Question 884149: Please answer using the 1st eight rules of formal logic
1. N ⊃ (D � W)
2. D ⊃ K
3. N / N � K

Click here to see answer by jim_thompson5910(35256)

Question 884279: 1)Provide counterexamples to the following statements.
a) Every geometric figure with four right angles is a square.
b) If a real number is not positive, then it must be negative.
Click here to see answer by richard1234(7193)

Question 885090: F>(~A.I)
Av(~J.F)
F
/~J
Click here to see answer by jim_thompson5910(35256)

Question 886091: NEED HELP ASAP PLEASE
Proof #1 (DIRECT PROOF ONLY)
Click here to see answer by richwmiller(17219)

Question 886098: NEED HELP ASAP PLEASE
Click here to see answer by richwmiller(17219)

Question 886097: Need help asap please
Click here to see answer by richwmiller(17219)

Question 886095: Proof # 2 (DIRECT PROOF ONLY)
Click here to see answer by richwmiller(17219)

Question 886094: NEED HELP ASAP PLEASE
Click here to see answer by richwmiller(17219)

Question 886984: Alright, I have access to rules: 1.Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Constructive dilemma 6. Simplification 7. conjunction 8. addition 9. demorgan 10. commutative 11. associative 12. Distribute 13. Double negate 14. transposition 15. Implication 16. equivalence 17. exportation 18. tautology
You may also use Indirect or conditional proof on this..
Please help with this:
~I
~(IvS)>K
/~S>K
Click here to see answer by jim_thompson5910(35256)

Question 887002: Hello, I have access to rules: 1.Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Constructive dilemma 6. Simplification 7. conjunction 8. addition 9. demorgan 10. commutative 11. associative 12. Distribute 13. Double negate 14. transposition 15. Implication 16. equivalence 17. exportation 18. tautology
Please help with this:
F>(P>N)
~N*~~P
/~F

Click here to see answer by jim_thompson5910(35256)

Question 890505: The question is related to Maxima and Minima in Differential calculus : The question is :
" The sum of the surface areas of a sphere and a cube is given. Show that when the sum of their volumes is least , the diameter of the sphere is equal to the edge of the cube."
Please send the step by step solution.
Regards,
Khoka123
Click here to see answer by Fombitz(32388)

Question 890514: The question is as under :
" The sum of the surface areas of a sphere and a cube is given. Show that when the sum of their volumes is least, the diameter of the sphere is equal to the edge of the cube."
The above question is related to Maxima and Minima chapter of Differential calculus.
Please send step by step solution.
Regards,
Khoka123.
Click here to see answer by Edwin McCravy(20055)

Question 890510: The question is related to Maxima and Minima chapter of Differential calculus. The question is as under :
" Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere."
Please send step by step solution of the above question.
Regards,
Khoka123
Click here to see answer by Edwin McCravy(20055)

Question 890509: The question is as under :
" Alight house is located at A, 2 km off-shore from the nearest point O on a straight beach and a shop is located at B. The shop is located on the beach , 4 km distant from O. If the housekeeper can row at the rate of 4 km/hour and walk at the rate of 6 km/hr, where should he plan to reach the shore, so as to cover the distance to the shop in the least possible time ? "
The question is related to maxima and minima chapter in differential calculus.
Please send step by step solution of the above question.
Regards,
Khoka123
Click here to see answer by josgarithmetic(39617)

Question 892962: The grades of Javed in nine monthly tests were 58, 56, 58, 64, 80, 56, 90, 80. The mode of his grades is
Click here to see answer by Fombitz(32388)

Question 893095: The table below shows the scores of students in a certain exam of a class of size 20.
Scores
30
45
50
55
Number of students
6
4
4
6
The average score of the class was
Click here to see answer by novice(7)

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