What is Logic: Definition and 1000 Discussions

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. adjacent

    What is the Answer to 1/3(10) using Logic?

    Homework Statement ##\frac{1}{2}(5)=3## , based on this logic, what is ##\frac{1}{3}(10)##? The Attempt at a Solution In real life, ##\frac{1}{2}(5)=2.5## so 2.5 --> 3 Just like that, ##\frac{1}{3}(10)=\frac{10}{3}## so 2.5 --> 3 10/3 -->x Cross multiply--- x=4 I am not very...
  2. G

    TTL - Is there a logic gate or IC that does this?

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  3. fluidistic

    C/C++ Why Does My C++ Code Result in an Infinite Loop?

    I don't understand why I enter in an infinite loop with the following code: #include <iostream> //for cout #include <cstdlib> //for rand() #include <ctime> // for time() #include <fstream> //to write into a text file using namespace std; static const int M = 3; ofstream myfile; int...
  4. J

    A question about the logic of making a "Snake" game

    I've started to make a "Snake" game (example: http://www.kongregate.com/games/uchiha/classic-snake-game) and reached a dead end. I'm not sure the programmatically best way of figuring out where the snake's "food" should next appear. It should of course appear anywhere on the screen that doesn't...
  5. QuarkCharmer

    Boolean logic expansion issue (POS -> CPOS)

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  6. R

    Exploring the Logic of Black Absorption: Ryan's Experiment

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  7. N

    Engineering Multiphase clock generator circuit and control logic

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  8. W

    Please help me refine a dissertation topic in mathematical logic

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  9. C

    MHB Simplify Logic using One Connective: Solving ((q→p) ^ (p→r))→(r→q)

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  10. D

    MHB Un-clear proof of my professor - logic and theory set

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  11. V

    MHB Value of x After Logic & Math Task w/ x=2

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  12. R

    Why Does the Firing Angle Equation for FC-TCR Not Work in MATLAB?

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  13. M

    IC Testing for Logic Gate Errors

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  14. P

    Can a State Diagram Repeat a State Twice in a Sequence?

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  15. E

    Understanding Logic Behind x=0: Explained

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  16. T

    Simplifying Digital Logic Equations: Using Karnaugh Maps and 2x2 Method

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  17. T

    Digital logic - Boolean algebra simplification problem

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  18. T

    Boolean Algebra Question (Digital Logic Circuits)

    Homework Statement The Attempt at a Solution Is my solution correct or can I simplify it even further?
  19. D

    Consecutive logic gates voltage loss

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  20. B

    How can permutations help with logic gates and circuit design?

    Hello, today in class we started a topic on permutations and combinations and I have come across a way in which it could be of use to me whilst working with 'logictutor' (a premade circuit board used to teach simple logic circuits). We have an experiment tomorrow where we will investigate...
  21. K

    Set Theory Logic: Finding True Statements in a Given Domain

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  22. S

    Solving a riddle using Boolean logic

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  23. P

    Few propositional logic questions

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  24. G

    Digital Logic - Tri State Buffers

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  25. A

    Why translating language to propositional logic is tough?

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  26. A

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  27. N

    Does Godel's theorem imply mathematics is more than logic?

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  28. G

    MHB Can the premise P∨Q be ignored in a propositional logic proof?

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  29. A

    What are the premises and conclusions in logic deduction problems?

    Homework Statement Homework Equations The Attempt at a Solution I don't understand the problem. For #41, which are the premises and which are the conclusions?
  30. G

    MHB Proving $(\neg P \to \neg Q) \to (Q \to P)$ in PL

    I'm trying to prove $$ : (\neg P \to \neg Q) \to (Q \to P)$$ in PL. Here's my attempt: $ \left\{1\right\} ~~~~~~~~~~ 1. ~~~~~~ \neg P \to \neg Q ~~~~~~~~~~~~~~~~~~~~~~ \text{Premise}$ $ \left\{2\right\} ~~~~~~~~~~ 2. ~~~~~~ Q ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{Assumption for CP}$...
  31. S

    Predicate logic - true or false formulae

    Hello everyone, I can't seem to understand how to do this question. Determine whether the formula F: ∃x∀y(P(x) → x = y) is true or false under each of the following interpretations over the domain D = {a, b}. (i) both P(a) and P(b) are true; (ii) both P(a) and P(b) are false; (iii) P(a) is...
  32. PrincePhoenix

    Logic Design: Interpreting entering and leaving a room.

    Homework Statement Hello. We have been given a project in our course "Digital Logic Design", which is an introductory course to Digital Logic. We are only allowed to use gates, multiplexers, flip-flops/latches, counters, comparators, simple displays (like seven segments) etc. I am making...
  33. N

    Potential energy: where is the error in my logic?

    1) For gravitational potential energy: ##F(r)=-\frac{\gamma M m}{r^2}##. 2) For potential energy of a conservative force-field: ##-\nabla E_p = F##. So the gradient of the potential energy is always equal to the force in that direction, just with the opposite sign. So when you move in the...
  34. Barioth

    MHB Logic, proving theorem in formal system K

    Hi here is the problem I'm working on, Let $A(x_1)$ be a well formed formula of a language $L$ in which $x_1$ is free, let $a_1$ an invidual constant of $L$, Show that the formula $A(a_1)\rightarrow(\exists x_1)A(x_1)$ is a theorem of $K_L$ on this link, the first slide as the axiom of $K_L$...
  35. Barioth

    MHB Determine if a Term is Free: Logic for Mathematicians

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  36. V

    Do We Assume Logic for Mathematics?

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  37. T

    Is an Intro to Logic Class Helpful for Transitioning into Higher Mathematics?

    Alright, so I will be registering for classes at my community college here in a few days and I am having a hard time deciding on classes. I am hoping to major in mathematics or physics (leaning toward pure math) and I hope to transfer to UC Berkeley (I have a 3.7 first semester) Some of the...
  38. A

    Building Converters using Logical Gates for 4-bit Inputs

    Homework Statement I have to build some converters (only for 4 bits) and i didn't understand how. How do i proceed? Which logical gates combined in such a way give me the y3y2y1y0 answer for x3x2x1x0? For example, build a coverter from EXCES3 to BCD, or from GRAY TO BCD, or C1 complement to C2...
  39. Z

    How Can Boolean Polynomials Determine Consistency in Propositional Formulas?

    My professor wants to convert propositional statements such as X ^ Y into polynomeals such as P[(X^Y)] = xy Now, we may have multiple propositional formulas and wish to determine if they are consistent or inconsistent using Boolean polynomials. I'm having a tough time finding material...
  40. D

    Question on the logic of rational roots theorem

    this is not a homework question, but rather I feel like there is a contradiction in the theorem and just want clarity. I know the theorem is correct so I am looking for help in where the mistake is in my logic. take f(x) = x^3 + x^2 - 4x- 7 the rational roots theorem says if there are any...
  41. B

    MHB Can You Solve This Set Theory and Binary Number Problem?

    Preparing for an upcoming midterm and this is one of the practice questions from an old test. The Question: Let X be a set with n elements, say S = {s1, s2,..., sn} Let B be the set of binary numbers with n digits. That is, sequences of n terms, each of which is 0 or 1. Define f : P(S) --> B...
  42. P

    Propositional logic question

    Negate ## [\neg (p\wedge \neg q)]\wedge \neg r ## and relpace the resulting formula by an equivalent which does not involve ## \neg, \vee, \wedge ## attempt: ## \neg ([\neg (p\wedge \neg q)]\wedge \neg r) = \neg \neg (p \wedge \neg q) \vee \neg \neg r ## ## = (p \wedge \neg q) \vee r...
  43. Z

    Logic Homework: Inconsistent + Consistent statements in Boolean logic

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  44. Q

    Logic Question; Molecular Shapes

    Homework Statement Number 17: http://i.minus.com/jbqSc694thPeBA.jpg Homework Equations I'm not even sure where to start. The Attempt at a Solution I know that tetrahedral shapes are non-polar if all of the attached elements are the same (e.g. CH4 or CCl4). I know all the answer...
  45. S

    Understand the logic behind the subtraction of 0

    Homework Statement Problem: Prove that if ##lim_{n→+∞} s_n## = ∞ and ##s_n## ≠ 0 for all n, then ##lim_{n→+∞} 1/s_n## = 0. Solution: Consider any ϵ > 0. Since ##lim_{n→+∞} s_n## = ∞, there exists some positive integer m such that, whenever n ≥ m, ##|s_n|## > 1/ϵ and, therefore...
  46. Vahsek

    Is it worth studying mathematical logic?

    I want to address this post primarily to people who have already studied mathematical logic, or are currently studying it. Since a while I've immersed myself in studying some math, and I must say that I started to enjoy pure mathematics. However, sometimes I don't really feel comfortable...
  47. R

    Engineering Diode logic doubt (digital circuit)

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  48. H

    Engineering Logic Circuit Design Homework Solutions

    Homework Statement 1. A nuclear power plant contains three danger sensors X, Y and Z that can shut down the plant. Sensor Z is in such a senstive location that it has a backup B. The plant is to be shut down if two of the three sensors indicate danger. However, with exception, sensor Z is...
  49. B

    Designing a CPU Using Multimedia Logic - Need Advice

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  50. C

    Need help in simplifying circuits with logic gates

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