Logic Definition and 1000 Threads

Logic (from Greek: λογική, logikḗ, 'possessed of reason, intellectual, dialectical, argumentative') is the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises). More broadly, logic is the analysis and appraisal of arguments.There is no universal agreement as to the exact definition or boundaries of logic (see § Rival conceptions). However, the scope of logic (broadly construed) includes:

The classification of arguments.
The systematic analysis of logical forms.
The systematic study of the validity of deductive inferences.
The strength of inductive inferences.
The study of faulty arguments, such as fallacies.
The study of logical paradoxes.
The study of syntax and semantics of formal languages.
The study of the concepts of meaning, denotation and truth.Historically, logic has been studied mainly in philosophy (since Antiquity), mathematics (since mid-19th century), and computer science (since mid-20th century). More recently, logic has also been studied in linguistics and in cognitive science. Overall, logic remains a strongly interdisciplinary area of study.

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  1. U

    Solving Logic Problem: Pizza & Students

    I have a problem that states: Write each english sentence in symbolic form using the following predicates: m = Melissa p = Pizza S(x) = ' x is a student ' L(x, y) = ' x likes y ' E(x, y) = ' x eats y ' Take A as the universal quantifier in this problem and M as the existential...
  2. P

    The logic problem faced in linear algebra

    I have some difficulties to understand the logic of the solution to this problem. Q:The graph of a(x2 +y2)+bx+cy +d = 0 is a circle if a 6= 0. Show that there is a circle through any three points in the plane that are not all on a line. solution:Insisting that the graph of...
  3. H

    Problems with probably very simple logic question

    Homework Statement The Island of Knights and Knave, where knights never lie; knaves lie always (that is, every statement made by a knight is rue, every statement made by a knave is false). a) Suppose you meet two islanders and ask who they are. One of them says "if i am a knight then so is my...
  4. Dembadon

    Logic: Possible Typo in Textbook

    It's possible that I'm not understanding the diagram and their reasoning, but I wanted to check with some people here before I come to a conclusion. Homework Statement Homework Equations The Attempt at a Solution I don't understand why the book says the formula is false, yet there is a "T"...
  5. P

    Logic Gates (OR and AND) Wave Form Diagrams

    If you take a look at the attachment that I have posted, you will see 4 wave diagrams labeled A, B, C, D, respectively. My objective to is to answer the questions after the A-D diagrams. The first one is a AND logic gate with A and B. So how would I combine A and B. Do I draw only the highs of...
  6. T

    Logic confusion - formally clear but practically not so.

    Hello everyone! This is a pretty strange question, perhaps. I've studied logic and know very well the difference between A --> B and B --> A. However, there's a specific problem that I often encounter in proofs in maths that I find strange. For example: you get a certain P.D.E. and want to...
  7. J

    Mod. Arithmetic Proof: I don't see flaws in my logic, but it isn't working out.

    1. Homework Statement . 1. Let a and b be constant integers with a \not = 0, and let the mapping f : Z \rightarrow Z be defined by F(x) = ax + b. Determine all values of a such that f is a bijection. Prove that the aforementioned values are the only possible values resulting in a bijection. The...
  8. W

    Solve Integer Sequence: 1955th Place = 4?

    Homework Statement All integers beginning with 1 are written down in succession. What digit is in the 1955th place? Homework Equations The Attempt at a SolutionI'm pretty sure it is 4 Wondered if someone wants to double check
  9. A

    Identifying Gate Logic Symbol on Spec Sheet: Digital Fundamentals Paper

    Hi there I'm currently doing a digital fundamentals paper and I was wondering if anyone could identify a logic symbol on the spec sheet attached, and what's it used for. It's on page 4, and the logic symbol is a diamond that is surrounded by 4 traingles. Theres eight of them and it's near...
  10. A

    Question about a logic notation

    (x∈R → f(x)>0) → f is asmani. What does it mean: 1. If there exists some x in R such that f(x)>0, then f is asmani. 2. If for all x in R we have f(x)>0, then f is asmani. 3. It's ambiguous or meaningless. 4. ...? Thanks in advance.
  11. S

    Simple Boolean Algebra / Propositional Logic Question

    Homework Statement Produce the given truth table (given below as well as in a neater version in the attached Excel document) using the Boolean operators AND, OR, and/or NOT: A (Input 1) B (Input 2) O (Output) 1 1 0 1 0 0 0 1 1 0...
  12. R

    Tips on Becoming Better at Logic?

    What are some ways you intertwine logic into syntax, so the two can work together? Does pseudo code help?
  13. J

    Help with Logic: Deducing Argument Form in Formal Language

    Hi there. I need help deducing an argument form in formal language, but I am not sure that I can communicate the example very well, nor even that it can be expressed in a formal language for that matter. The case at hand: Rene is a cat. Julie is not a cat. Therefore, julie is a...
  14. A

    Do superpositions violate conventional logic (philosophy)?

    I recently read a research summary about using magnetic fields to briefly maintain quantum states in relation to quantum computing. The article makes reference to "a" simultaneously being "a" and "not 'a'". I'm left wondering how the concept of superposition is reconciled with conventional...
  15. P

    Logic and creativity within mathematics

    I've always been a creative person since I was little. I really wasn't noticed for my potential for maths at all when I was growing up and it was a year before I completed my GCSE's I was stuck in set 2 maths with a predicted grade of a D but tried and got a B all in all. When I went into...
  16. mrspeedybob

    Trying to find the error in my logic or math. Deceleration of a car.

    So I got a ticket a few days ago for running a red light, the yellow light was very short, I'm trying to figure out if the city set the yellow light too short to be reasonable. The speed limit at that location is 50 mph, the yellow light is 4 seconds. Federal motor vehical safety standards...
  17. V

    Why is slope represented as delta y over delta x?

    Homework Statement You always see slope represented as \frac{\delta y}{\delta x}. Is there any particular reason for why the change in "y" is in the numerator and the change in "x" in the denominator? Why couldn't we represent it as delta x over delta y? Homework Equations \frac{\delta...
  18. D

    Use of input current and quiescent supply current in logic gates

    What is the meaning and use of input current in logic gates? Also meaning and use of quiescent supply current.
  19. A

    Predicate logic inference problem

    Homework Statement Consider the following question Adams is a boy who does not own a car. Mary dates only boys who own cars.Therefore Mary does not date Adams. Homework Equations The Attempt at a Solution My answer is like this... Let Bx=x is a boy. Ox=x owns car...
  20. N

    Does a logic with set of all sets exist?

    Hello. As I understand, in the classical logic it's impossible to "take", for example, the set of all sets. I was wondering: is it possible to create a logic where that is possible by changing some of the basic postulates by which logic works? Or is it impossible for all logics? Thank you.
  21. T

    Which Curve Meets Its Target Value First?

    Here's the issue. I have two curves that are dependent on each other (part of a bigger solution set). The logic of my program requires that one of two conditions have to be met. Basically, two curves are rising in y as x increases. Either curve 1 will reach some value "first", or curve 2...
  22. Shackleford

    Learning Logic and Truth Tables: My Algebra Journey

    I'm taking Abstract Algebra right now, and we just briefly covered Logic and Truth Tables. This is my first time in school to learn such things. http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110712_195458.jpg 37. I understand. 39. I understand. 41. I don't understand...
  23. T

    Can you recommend an epistemology book and a logic book?

    Hi, I'm looking for a book about epistemology and another about logic. But preferably books that aren't too technical, because I want to read them more as a hobby rather than as homework. But not too simple either please! On epistemology I found...
  24. T

    Lingusitics How could I translate logic reasoning to the language of mathematics?

    I don't know much about this subject, so this is probably a very basic question. If I want to understand/explain something, I use inductive or deductive reasoning, which are parts of logic. For example, take this inductive reasoning: Every life form we know of depends on liquid water to exist...
  25. B

    Inconsistency In Sentence Logic and in Predicate Logic

    Does anyone know/understand the different definitions for Inconsistency in Sentence Logic and in Predicate Logic? I know in Sentence Logic, that a sentence ( a Wff, actually) S is contradictory, if from S we can derive (using theorems of truth-functional logic ) a sentence of...
  26. romsofia

    Exploring Logic in Math Research

    How exactly does math research work? Thanks for all the help! EDIT: Since it may vary by field, I'm asking about the logic area.
  27. Q

    Logic Image Test Homework: B or E?

    Homework Statement [PLAIN]http://img863.imageshack.us/img863/6634/quiz14.jpg Homework Equations None The Attempt at a Solution I say B or E but I can't find a reason to choose. I ignore the solution.
  28. O

    Combinational Logic High for Range

    I need to use combinational logic to produce a high ouput for a certain range of values. I have and anaolgue signal which i have converted to a 12 bit digital signal, I need an LED to be turned on when the analogue signal is above a certain voltage. I have the digital value (101001110100 =...
  29. O

    Mathematical Logic by Cori and Lascar: Incomplete proof of Lemma 1.9?

    "Mathematical Logic" by Cori and Lascar: Incomplete proof of Lemma 1.9? I have a question on the book "Mathematical Logic: Propositional calculus, Boolean Algebras, predicate calculus" by Rene Cori and Daniel Lascar. Proof of Lemma 1.9 given on...
  30. O

    Mathematical Logic by Cori and Lascar : Possible typo?

    I have a question on the textbook "Mathematical Logic: Propositional calculus, Boolean Algebras, predicate calculus" by Rene Cori and Daniel Lascar. This is not about an exercise but about the conceptual content of the book. So I did not post this in the "Coursework and Homework questions"...
  31. N

    How important is a solid understanding of Logic

    How important is a solid (or better) understanding of Logic, especially Symbolic and Mathematical, for an aspiring mathematician? For a physicist? Other scientists? Are there variations in how important it is for Analysis, Topology and Algebra? A mathematically inclined physicist told me...
  32. S

    Can someone explain the following logic used to define the meter?

    "The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.Note that the effect of this definition is to fix the speed of light in vacuum at exactly 299,792,458 m/s." I don't understand this because how can you use a number based on...
  33. S

    Looking for a Detailed Explanation of How Transistors and Logic Gates Compute

    Hi, I've looked everywhere for an explanation of this, including this forum, and none of them seem to satisfy the level of detail I am looking for. More specifically, I am interested in how processing units used a fixed setup of logic gates and transistors to perform universal computation...
  34. pairofstrings

    How can compilers be used to implement logic gates and IDEs?

    I want to find out how computer language compilers works from hardware point of view. How logic gates are implemented using compilers? Can anyone suggest me a good reference book or website where I can find this information?
  35. Mentallic

    Is Starting With Assumption of Truth A Valid Proof Strategy?

    The question was to prove \sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}>1, x>1 And I had two choices to go about this, I could have manipulated the expression \sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}} by multiplying numerator and denominator by its conjugate, squaring, manipulating etc. and getting an...
  36. Fredrik

    The logic of a physical system

    In both classical and quantum mechanics, there's a lattice called the logic of the physical system. In CM, it's the set of all subsets of phase space. In QM, it's the set of all closed subspaces of a Hilbert space. Sloppy presentations of this subject say that the members of the logic represent...
  37. D

    Engineering Solving Diode Logic Circuits: 4V, B=2V, C=3V

    EDIT: I was being stupid and forgot the first diode would turn off after i worked out stuff for diode C, thanks anyway, solution found!Hi I'm having some trouble getting the correct output voltage when i model the diodes using a voltage ofset and resistors. A = 4V, B = 2V, C = 3V Using Voltage...
  38. T

    What should I know to test out of Intro to Logic and Proof?

    Half of the classes I want to take have it as a prereq, and it's not offered over the summer. Assuming my school allows it, I want to try to test out. What should I know to be prepared? Thanks, Tyler
  39. J

    Why do some propositions defy logical proof?

    I recently read about the unexpected hanging problem and I was so surprised that logic actually failed in determining the solution!:( Is this just an isolated exception, or are there more paradoxes like this? And more importantly, why does logic fail? Isn't there any way around this? I just...
  40. L

    Investigating Logic Behind Line Segment Lengths

    I am confused ,whats wrong with the reasoning below ? assume that the black lines are parallel and red Line segments are defined between the black lines. for any point on one of the red line segments there exist only one point on the other one (the points that are touched by the lines...
  41. M

    Predicate Logic Universal and Existential quantifiers

    Hi, I'm taking an intro logic class and though I'm comfortable with most propositional logic, predicate logic is confusing me. I joined the forum to ask this particular question that I've been stuck on for a while. Any help would be appreciated - I'm having trouble finding information on the web...
  42. H

    Trouble with a proof in propositional logic

    Greetings everyone, I have been teaching myself mathematical logic for amusement by going through Stephen Cole Kleene’s textbook, “Mathematical Logic”. I am stuck on the following problem (problem 13.2 on page 58, if you happen to have the book): Show that, if |- Am+1, then A1, … , Am |- B...
  43. Artlav

    Diode-transistor logic shortcuts?

    Greetings. I'm making some experiments with DTL circuits, and i wonder if i missed something obvious when piecing the bits and facts about it from around the net. Are there ways to reduce the number of elements in the circuit when multiple DTL gates are used? For example, here is a NAND...
  44. W

    What is the logic behind this image?

    http://www.roo7oman.com/up/files/240379.jpg
  45. B

    Programmable logic device question

    I don't know a lot about PLD's so hopefully someone here can help me. Is there a relatively cheap PLD that can switch between 2 inputs every given amount of time, like every second or every 5 seconds? I'm just trying to find what I am looking for and can look up and read through the data...
  46. T

    Solving Logic Function w/ NOR Gates

    Homework Statement Consider the truth table below. (a) Write an expression for the logic function that it represents, and simplify that expression as much as possible, showing all steps. (b) Draw a logic circuit implementing this. (c) Redesign your circuit to use only NOR gates...
  47. B

    Does Adding HCl Change the pH of a CH3COOH/CH3COO Buffer?

    Calculate final pH of 25 ml buffer 0.1 M CH3COOH/CH3COO, pH=3.50, after the addition of 1.00 ml of 0.1 M HCl. 3.50=4.75+log(base/3.16x10-4) Base = 1.78x10-5 M Acid = 3.16x10-4 M Mole base = 0.000712 - 0.0001 = 0.000612 Mole Acid = 0.01264 +0.0001 = 0.01274 Mole Acid...
  48. I

    Solving Boolean Logic Expressions with And, Or and Not Gates

    The three equations below represent three different logic expressions using and, or and not gates of two boolean variables A and B. A boolean variable can take only one of two possible values: True or False. Which of the two expressions are identical, meaning that for any combination of A...
  49. F

    Seeking Alternatives for Microsoft Visio 2010 for Detailed Computer Logic Diagrams

    Hello, I want to draw the detailed logic level diagram for a basic computer. For this i found a software that will work which is microsoft visio 2010. But i m not satisfied with that because it has some limitations. Such as re-arranging the wires automatically and also the simulation...
  50. R

    My logic vs. Calculated Results: Plots of Thrust, RPM, Spillage

    I finally figured out what my previous problem was in my last question posted. I have obtained the plots required but I am a little confused about the trends. (1) At low Mach, should my thrust be lower compared to the value at a higher Mach? (2) Should the RPM decrease with an increase in...
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