# Questions on Logic: Proofs answered by real tutors!

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 Logic: Proofs Solvers Lessons Answers archive Quiz In Depth

## Tutors Answer Your Questions about Proofs (FREE)

 Question 524132: There is a famous theorem in Euclidean geometry that states that the sum of the interior angles of a triangle is 180 degrees. a)Use the theorem about triangles to determine the sum of the angles of a convex quadrilateral. Hint: Draw a convex quadrilateral and draw a diagonal. b) Use the result in Part(1) to determine the sum of the angles of a convex pentagon. c) Use the result in Part(2) to determine the sum of the angles of a convex hexagon. d)Let 'n' be a natural number with 'n'> or = to 3. Make a conjecture about the sum of the angles of a convex polygon with 'n' sides and use mathematical induction to prove your conjecture. ** I've figured out a, b, and c. I've also created a conjecture for d. Here's what I have: "Let 'n' be a natural number with 'n'> or = to 3. For any convex polygon with 'n' sides, the sum of the angle of the polygon is 180(n-2)". I have my basis class which is when n=3 then the sum = 180 degrees, but I don't know how to prove my induction step. I know (k+1) must be substitued in for 'n' at some point but not sure when and what to do. Please help. Click here to see answer by stanbon(57224)

 Question 527300: Disprove: If a, b, and c are integers such that a does not divide b and c does not divide d, then a+c does not divide b+d Click here to see answer by richard1234(5390)

 Question 527290: Prove : If m is an odd integer, then 4 divides m^2 +2m+5 I have gotten this so far but i dont know if its right and how to finish working it out! Proof: Let m be an odd integer there is an integer such that m=2k+1 then m^2 +2m +5 = (2k+1)^2 + 2(2k+1) +5 then m^2 + 2m +5= (4k^2 +4k +1) + (4k+2) +5 then m^2 +2m +5= (4k^2 +4k+4k) +1+2+5 then m^2 +2m +5 = 4(k^2 +k+k) + 8 Click here to see answer by richard1234(5390)

 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 solver91311(16868)

 Question 535731: (4x10^3)(6x10^x)/2.4x10^-4=1 Determine the value of x that makes the statement true Click here to see answer by fcabanski(872)

 Question 536807: 1.) (K>K) > R 2.) (RvM) > N /N I need to use either AIP or ACP (or both) and the eighteen rules of inference to derive the conclusion. If someone can please help. Click here to see answer by jim_thompson5910(28476)

 Question 537651: prove that m = y/x-b/x Click here to see answer by Alan3354(30966)

 Question 539115: Find the error in this proof that 2=1. x=y X^2=xy X^2-y^2=xy-y^2 (x+y)(x-y)=y(x-y) ((x+y)(x-y)/(x-y))=(y(x-y)/(x-y)) X+y=y Y+y=y 2y=y (2y/y)=(y/y) 2=1 Click here to see answer by Mathpassionate(25)

 Question 542472: Please help with this logic proof: 1. S v B 2. B -> D 3. S -> G conclusion D v G Click here to see answer by Theo(3458)

 Question 542785: i don't know where to begin p -> (q v r), (p -> r) -> (s & t), q -> r /t Click here to see answer by Edwin McCravy(8880)

 Question 544773: If a is a irrational number and b is an rational number, prove that either (b − a) or (b + a) is irrational. Click here to see answer by richard1234(5390)

 Question 548064: Prove that the function is bijective. The function is f: N--->Z f(x)=(1+(−1)^x * (2x − 1)) /4 I tried to attempt it using induction. I did a base case for subjectivity of f(1) and f(2) and it worked. Then I tried to substitute k+1 for x but I have gotten stuck. Click here to see answer by richard1234(5390)

 Question 549344: Make a logic proof sentence Click here to see answer by solver91311(16868)

 Question 551411: Given: If schools close, then workers will lose their jobs If we save fuel, then workers will not lose their jobs We save fuel or there is an energy crisis Schools will close PROVE: There is an energy crisis Click here to see answer by Theo(3458)

 Question 561663: 3 apples cost 45 cents. how much would 15 apples cost?(in dollars) Click here to see answer by josmiceli(9650)

 Question 562200: There is a famous theorem in Euclidean geometry that states that the sum of the interior angles of a triangle is 180. (a) Use the theorem about triangles to determine the sum of the angles of a convex quadrilateral. (b) Use the result in Part (1) to determine the sum of the angles of a convex pentagon. (c) Use the result in Part (2) to determine the sum of the angles of a convex hexagon. Click here to see answer by richard1234(5390)

 Question 563757: Can you please help me with this probability question... A person spins the pointer and is awarded the amount indicated by the pointer. It costs \$5 to play the game. The diagram shows a circle divided into 3 parts. The pointer points to the 1/2 section marked \$2. The 1/4 section is marked \$20, and the other 1/4 section is marked \$5. Determine: The expectation of a person who plays the game. The fair price to play the game. Click here to see answer by stanbon(57224)

 Question 566235: Prove that the sum of any pair of rational numbers is a rational number. Click here to see answer by jim_thompson5910(28476)
 Question 566235: Prove that the sum of any pair of rational numbers is a rational number. Click here to see answer by richard1234(5390)

 Question 567801: Proposition 1.8 If m is an integer, then (-m)+m=0 Proof Let m be an element of Z There exist a (-m) in an element Z Axiom 1.4 such that m+(-m)=0 m+(-m) = (-m)+m Axiom 1.1(i) = 0 Q.E.D That's how I assume it is proven but it would be nice if someone could double check and make sure it is correct and also correct it. Thanks Click here to see answer by richard1234(5390)

 Question 568394: 1. ~H 2. H v K 3. L >H 4. ~(K.~L) v (~L.M) / M Click here to see answer by jim_thompson5910(28476)

 Question 569226: Please help me prove: -a = (-1)*a Thank you. Click here to see answer by stanbon(57224)

 Question 569235: Please help prove "if x < y, then -y<-x" Click here to see answer by jim_thompson5910(28476)

 Question 571456: Each student at Sussex Elementary School takes one foreign language. Two thirds of the students take Spanish, 1/9 take French, 1/18 take German, and the rest take some other foreign language. if there are 720 students in the school, how many do not take Spanish, French, and German? Click here to see answer by josmiceli(9650)

 Question 574686: Decide whether or not the following proposition is true. If it is false, demonstrate this by presenting a counterexample. If it is true, decide whether or not the proof is correct. If the proof is not correct, rewrite the proof so that it is correct. If the proof is correct, decide whether or not it is well-written and revise the proof, as needed, so that it is well-written. Proposition. For each natural number n with n > 2, it is true that 2n > 1 + n. Proof. We let k be a natural number and assume that 2k > 1 + k. Multiplying both sides of this inequality by 2, we see that 2k+1 > 2 + 2k. However, 2 + 2k > 2 + k, and hence, 2k+1 > 1 + (k + 1). By mathematical induction, we conclude that 2n > 1 + n. Click here to see answer by solver91311(16868)
 Question 574686: Decide whether or not the following proposition is true. If it is false, demonstrate this by presenting a counterexample. If it is true, decide whether or not the proof is correct. If the proof is not correct, rewrite the proof so that it is correct. If the proof is correct, decide whether or not it is well-written and revise the proof, as needed, so that it is well-written. Proposition. For each natural number n with n > 2, it is true that 2n > 1 + n. Proof. We let k be a natural number and assume that 2k > 1 + k. Multiplying both sides of this inequality by 2, we see that 2k+1 > 2 + 2k. However, 2 + 2k > 2 + k, and hence, 2k+1 > 1 + (k + 1). By mathematical induction, we conclude that 2n > 1 + n. Click here to see answer by richard1234(5390)

 Question 582129: 1. A > [B>(C*~D)] 2. (BvE)>(DvE) Therefore, 3. (A*B) > (C*E) Using conditional proof and 18 rules derive the conclusion to prove it is valid Click here to see answer by jim_thompson5910(28476)

 Question 582293: I am more than 100 but less than 200. I am divisible by 5. The sum and product of my digits are divisible by 5. My three digits are odd. Which number am I? Click here to see answer by Edwin McCravy(8880)

 Question 582497: Please help me solve this using indirect proofs! (I can't get it go anywhere it seems!) Thank you!! Premise 1. B > [(O v ~O) > (T v U)] Premise 2. U > ~(G v ~G) Conclusion: B > T Click here to see answer by jim_thompson5910(28476)

 Question 585493: 1. (E∨F)→~G 2. ~H 3. H∨K 4. (K∨L)→E ∴ ~G Click here to see answer by jim_thompson5910(28476)

 Question 588387: I am trying to work on the following proof. I know I used DEM incorrectly on line 3. I cannot figure out what other rule to use. I tried contraposition, but it does not allow me to break down the lines. I cannot use MT or MP without having x or y by itself. I do not know what other conditional rule to use. 1. X > Y / X . Z > Y 2. ~X v Y CE 1 3. ~X . ~Y DEM 3 4. ~X Simp 3 5. ~Y Simp 3 6. X DS 2,5 7. Y DS 2,4 8 X v Z Add 6 9. Z DS 4,8 10. ~X v Z Conj 4,9 11. X > Z CE 10 12. ~Z > ~X Contrap 11 13. ~Z MT 4,12 14. ~Z v Y Add 13 15. Z > Y CE 14 16. X . Z > Y Conj 6,15 thank you! Click here to see answer by jim_thompson5910(28476)

 Question 588757: Use truth tables to test the validity of the argument. p → ~q q → ~p ∴ p ∨ q Click here to see answer by jim_thompson5910(28476)

 Question 589689: what is the solution to this logarithm question. log3 to power of x=y=log9 to power(2x-1) Click here to see answer by ankor@dixie-net.com(15624)

 Question 591301: I'm having a hard time with some of my proofs: A>~A (~WvK)>A // W And this one: (~DvP)vN ~(PvN)vG // D>G Thank you Click here to see answer by jim_thompson5910(28476)

 Question 592846: INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises. Given the following premises: 1. ~N v H 2. Q > ~(~N v H) 3. (~N v Q) • (H > Q) A. Q v Q 1, 3, CD B. ~Q 1, 2, MT C. ~N > ~(~N v H) 2, 3, HS D. Q > (N • ~H) 2, DM E. H > Q 3, Simp Click here to see answer by jim_thompson5910(28476)

 Question 592849: INSTRUCTIONS: Select the conclusion that follows in a single step from the given premises. Given the following premises: 1. Q > (H • L) 2. H > ~Q 3. L > ~Q A. Q > ~Q 1, 3, HS B. (L > ~Q) • (H > ~Q) 2, 3, Conj C. (Q > H) > L 1, Exp D. H > L 2, 3, HS E. L > (H • L) 1, 3, HS Click here to see answer by jim_thompson5910(28476)

 Question 593872: Can you help me with this proof? (O>R)>S / (P>R)~S // ~R The > is a horseshoe. I've been at this all day and I can't even think of how to start. Click here to see answer by jim_thompson5910(28476)

 Question 593930: I can only use the 8 implicational rules 1. (A v ~B) >(F v (R . G)) 2. A 3. F > L 4. (R . G) > T 5. (L v T) > S :. S Click here to see answer by jim_thompson5910(28476)

 Question 593928: I can only use the 8 implicational rules. I've tried but can seem to get it. someone please help 1. (FvE)> ~D 2. SvD 3. E :. S Click here to see answer by jim_thompson5910(28476)

 Question 593929: I can only use the 8 implicational rules to solve this problem. 1. ~Fv~G 2. ~F > Z 3. ~G > ~R 4. (Zv~R) > (U > P) 5. ~P :. ~U Click here to see answer by jim_thompson5910(28476)

 Question 594150: I can only use the 8 implicational rules.Can someone please help me? 1. (Ev~B)>(~SvT) 2. E 3. ~S>L 4. T>~C 5. (Lv~C)>A :. A Click here to see answer by jim_thompson5910(28476)

 Question 594156: Can someone help me solve this please? I can only use the 8 implicational rules 1. Bv~C 2. B>E 3. ~~C :. ~BvE Click here to see answer by jim_thompson5910(28476)

 Question 594157: I can only use the 8 implicational rules 1. (AvG)>K 2. K>(B>F) 3. A∙B :. F Click here to see answer by jim_thompson5910(28476)

 Question 594158: 1. ~M 2. (~M∙~N)>(Q>P) 3. ~N 4. P>R :. Q>R Click here to see answer by jim_thompson5910(28476)

 Question 594160: i can only use the 8 implicational rules 1. ~W∙~~Z 2. (~W∙X)>Y 3. ~ZvX :. Y Click here to see answer by jim_thompson5910(28476)

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