Questions on Logic: Proofs answered by real tutors!

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 Logic: Proofs Solvers Lessons Answers archive Quiz In Depth

 Question 607197: How do you come to the conclusion of ~G given the following premises 1. G->(H->K) 2.(Hv~M)->~K 3. H Key: "->" means horseshoe (material implication) "v" means wedge (disjucntion) Click here to see answer by jim_thompson5910(28598)

 Question 607200: Could you please help me solve the following proof? I have worked a few lines after the conclusion but am stuck after that. 1. E>(S>T) 2. (~L*M) > (S*E) 3. ~(TvL) // ~M 4. (E*S) >T 1. Exportation 5. ~T*~L 3. DeMorgans 6. ~T 5. Simplification 7. ~(E*S) 4,6 Modus Tollens Key: > equals wedge * equals dot Click here to see answer by jim_thompson5910(28598)

 Question 607205: I have started the following proof but am not sure how to finish. thanks! 1. G>(H>K) 2. (Hv~M) > ~K 3. H // ~G 4. ~Gv(H>K) >equals horseshoe Click here to see answer by jim_thompson5910(28598)

 Question 607705: 1. S v (U*P) 2. (SvU)>R // R > equals horseshoe Click here to see answer by jim_thompson5910(28598)

 Question 607845: This may seem easy, but I don't get how to find the answer to this 1. F <-> G with the final answer of -F <-> -G Click here to see answer by jim_thompson5910(28598)

 Question 608105: 1. p>q 2. ~q /~p 3.?????? How do I get to the conclusion? I'm new at this and don't really understand it yet. I thought line 3 looked like this: 3. ~p 1,2, MT Click here to see answer by jim_thompson5910(28598)

 Question 608113: 1. pV(q . r) 2. ~p /q . r How do I get q . r? Thought line 3 was: (pVq) . (pVr) 1, Dist......Now I'm stuck and don't know how to get q . r Please help! Click here to see answer by jim_thompson5910(28598)

 Question 608115: 1. ~pVq 2. p /q 3.????? I figured line 3 is: ~p . ~q 1,DM ?? Then line 4: q 2,3 DS....Probably way off. Help is much appreciated! Click here to see answer by jim_thompson5910(28598)

 Question 607887: Determine by showing work and using any method whether argument is valid The number 91 is prime just in case it is not composite. The number 91 is not both prime and divisible by 2. The number 91 is divisible by 2. Therefore the number 91 is composite. Click here to see answer by richard1234(5390)

 Question 608410: Can you prove this identity: - = 2 Click here to see answer by Edwin McCravy(8909)

 Question 610046: my question is that i got the same conclusion as my instructor but with different methods and i was wondering if that is still ok. the instructions are to add just 2 statements to the premises to produce a formal proof of validity. ill provide my answers and his, thanks a lot. 1. (S.T) v (U.V) 2. ~S v ~T Therefore U.V My answer 3. (U.V) v (S.t) 1, Com. 4. U.V 3, Taut. his answer 3. ~(S.T) 2, Dem. 4. U.V 1,3 D.S. Click here to see answer by jim_thompson5910(28598)

 Question 613312: Write a formal proof of validity for the given arguments A) 1. (R>S) 2. V v~S 3. ~V/.'.~R B) 1. W.(XvY) 2. W 3. ~X/.'.YvZ C) 1. A * ~ B / .'. B > C Click here to see answer by jim_thompson5910(28598)

 Question 616027: Hi just needed some help in solving this equation it may be invalid so means that it can't be solved or it may be valid meaning it can be solved and I am stuck so not sure if I am right or not. Here it is: VxEy(Rxy) l- VxEy(Rxy & Ez(Ryz)) Thanks Click here to see answer by Alan3354(30993)

 Question 616557: 1. D 2. ~C 3. (A v B) -> C 4. [(~A • D) • ~B] -> (P -> Q) :. ~P v Q Click here to see answer by jim_thompson5910(28598)

 Question 617771: 1. R v ~T 2. ~T>O 3. ~O :. R Click here to see answer by jim_thompson5910(28598)

 Question 617774: 1. B > (C . D ) 2. R 3. B :. (C . D ) . R Click here to see answer by jim_thompson5910(28598)

 Question 617772: 1. (W . (R v T ) ) > P 2. ( P v L ) > ~ H 3. W 4. R :. ~ H Click here to see answer by jim_thompson5910(28598)

 Question 622920: The head of a fish is 9 inches long. The body length of the fish between the head and the tail is equal to the head plus the tail. The tail length is equal to the head plus one half of the body length between the head and the tail. This is enough information to work out that the total length of the fish is what? (Pencil and paper may be used.) Click here to see answer by KMST(1872)

 Question 626898: Construct a truth table for (p V ~q) ↔ p Click here to see answer by jim_thompson5910(28598)

 Question 627286: Is it possible that two different reasons can justify a step in a proof? Why or why not? Is it easier to work down the columns or across the rows in a proof? Why? Make sure you justify your opinion. Click here to see answer by solver91311(16897)

 Question 630377: Construct a truth table for q ↔ (p^ ~q) Click here to see answer by Theo(3464)

 Question 632553: In the same amount of time a new production assembly robot can assemble 8 times as many transmissions as an old assembly line. If the new robot can assemble 'x' transmissions per hour, how many transmissions can the new robot and the old assembly line produce together in five days of round the clock production. Click here to see answer by josmiceli(9697)

 Question 632981: When you square any integer, the last digit of the number you get will never be an eight. Is this statement true, false, or sometimes true. Justify your result. to prove this i've tried... 1^2=1 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2 = 100 as you can see this is true for single digits i've tried double digits as well up till 30^2, and clearly enough the last digit is never an eight. from what i've got above im guessing that this statement is true! Click here to see answer by Edwin McCravy(8909)
 Question 632981: When you square any integer, the last digit of the number you get will never be an eight. Is this statement true, false, or sometimes true. Justify your result. to prove this i've tried... 1^2=1 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2 = 100 as you can see this is true for single digits i've tried double digits as well up till 30^2, and clearly enough the last digit is never an eight. from what i've got above im guessing that this statement is true! Click here to see answer by richard1234(5390)

 Question 633618: I need help completing this proof. 1. R&S, S->(P->Q), Q->P |- P<->Q Click here to see answer by solver91311(16897)

 Question 636279: 28 liters oil in a pot how divide the oil in 15 liters pot and 28liters pot but each pot have 14 liters oils and also have a13liters pot, how tell me this possible Click here to see answer by solver91311(16897)

 Question 643819: Prove that |x + y| ≦ |x| + |y| Click here to see answer by AnlytcPhil(1277)

 Question 644513: Let S and T be sets. Prove that if x ∉ S ∩ T, then X ∉ S or X ∉ T. Click here to see answer by jim_thompson5910(28598)

 Question 644532: Prove or give a counterexample to each statement. ∀x ∈ ℝ, ((x^2) + 5x + 7 > 0) Click here to see answer by jim_thompson5910(28598)

 Question 644546: Prove or give a counterexample. S ∪ T = T ⇔ S ⊆ T Click here to see answer by jim_thompson5910(28598)

 Question 648551: the one by on step proof for a-(a-b)=2a-b Click here to see answer by swincher4391(726)

 Question 654642: Given: a --> c Prove: b ~a --> b ~c Click here to see answer by solver91311(16897)

 Question 659373: if x is a prime interger then x is odd Click here to see answer by Alan3354(30993)