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. P

    Proving/Disproving: Int x, y, z Divisibility Claim

    I wasn't sure if this went in math, or computer science. I'm posting it here, because it is for a computer science course, although it's technically mathematical proofs... 1. The problem: Prove or disprove the following claim: For all integers x, y, and z, if x does not divide yz then x does...
  2. bradzyc

    ASIC Logic Gates NAND Homework: Solving 2-Input NAND Gate Circuit

    Homework Statement Hi everyone, Very new to this forum so please bear with me! I have an assignment as part of my engineering course that I seem to be struggling with so I'm wondering if I can grab some help. Basically I have a water tank that feeds three separate processed (A, B, C). When...
  3. Alxb577

    Difficult Logic Gate Puzzle Using Only 2 Input NAND Gates

    Homework Statement [/B] Impliment the expression which is already in minimum sum of products form using only two-input NAND gates. No gate may be used as a NOT. All inputs are available both uncomplemented and complemented. (The number of gates required is shown in parentheses.) f = ab'd' +...
  4. S

    A discrete mathematics question about logic?

    Hey guys here is the question i'd appreciate if you could help me with it: it says that no one dies in planet X,some spies of planet Y were captured by planet X's police.They are so professional that won't say anything to police so their inspection will go on forever and their inspection has no...
  5. M

    Can Logical Inference Rules Prove This Propositional Argument?

    Homework Statement For each of the premise-conclusion pairs below, give a valid step-by-step argument ( proof ) along with the name of the inference rule used in each step premise { ¬ p → r ∧ ¬ s , t → s , u → ¬p , ¬w , u ∨ w } conclusion : ¬t ∨ w Homework Equations All...
  6. M

    Engineering Detector of even numbers in logic circuit

    Homework Statement I need to make a circuit that detects even numbers. Need to find the equation for F when input A and B are both even. Input A: Word of 5 -bit signed representation in complement 2. Input B: Word of 3 -bit signed representation in complement 2. Homework Equations for B...
  7. STEMucator

    Engineering Logic Circuit Conversion Homework: NAND-NOR to AND-OR and Back to NAND-NOR

    Homework Statement 1. Convert the following NAND-NOR circuit to simplest AND-OR circuit (bubbles allowed) such that the output gate is an AND. Then, convert the resulting circuit back into a NAND-NOR circuit (no bubbles) such that the output gate is a NOR. Homework EquationsThe Attempt at...
  8. M

    Logic Gates Algebra: Simplify A/B + /BC + /AB

    Homework Statement I am confused a little bit. I have been asked to simplify this function: A/B + /BC + /AB I seriously can't seem to know how to simplify this as for me its already simplified. Homework Equations N/A The Attempt at a Solution The best I could do is : (/A+/B) * (A+B+C) I did...
  9. M

    Engineering Building a logic circuit from a truth table

    P.S I know I am not supposed to use attachment but there are no way for me to input the table in a clean way... same for the logic circuit drawing. Would anyone mind helping me? 1. Homework Statement Homework Equations AND gates require both input to be True to get a true ouput NOT gates...
  10. L

    Converting logic diagram to only NAND gates

    Homework Statement How is he able to just swap the inverter for a NAND gate? Doesn't a NAND gate require two things? See the text on the right for his explanation [/B] Homework EquationsThe Attempt at a Solution
  11. Bhavin

    Engineering Need help in designing a logic circuit

    Design a circuit that will light the same number of LEDs as there are active switches. You will utilize three switches as input. The LEDs should be lit as a bar-magnitude display. The output pattern should look as follows: Active Input switch count LED bar-magnitude display (vertical) no...
  12. N

    Translating sentence into symbols

    I'm having trouble with translating this english sentence into logic symbols. The sentence is The numbers four and five aren't both prime, but the numbers five and seven are. I was thinking ~(F&I)v(IvS) but I really don't know how to deal with the "but". Thanks
  13. STEMucator

    Engineering Simplest Logic Circuit for z=0 with Inputs a, b, c

    Homework Statement Draw the simplest logic gate or circuit for the description below. The inputs are ##a, b, c## and the output is ##z##. ##z = 0## only if ##abc = 010## or ##abc = 110##Homework EquationsThe Attempt at a Solution So i drew up a quick table, AND and OR'ed the required terms...
  14. D

    Understanding Position Derivatives: Does Logic Follow?

    This might be a very vague and unclear question, but let me explain. When an object at rest moves, or moves from point A to point B , we know the object must have had some velocity (1st derivative of position) during that trip. It's also true that the object had to have accelerated to gain that...
  15. mishima

    Logic gate Simulation Software?

    Hi, I have used Digital Works and Logisim for doing things like building memory cells out of logic gates and general study of sequential logic. The free version of Digital Works does not work on my 64 bit windows computer at work, and Logisim does not offer all of the features of Digital Works...
  16. mishima

    Engineering Looking for great sequential logic text

    Hi, I have been through Alan Clements' Principles of Computer Hardware along with some online texts. I would like to purchase a comprehensive text on Sequential Logic at the undergraduate level. Having never studied this topic formally at university, I'm not sure how to discriminate between a...
  17. 22990atinesh

    Logic: All Comedians are Funny?

    Consider the predicates C(x)=x is a comedian F(x)=x is funny where domain=All people in the world Now consider the predicate logic ##1. \forall x [C(x) \rightarrow F(x)]## ##2. \exists x [C(x) \rightarrow F(x)]## Doesn't both the above predicate logic refers to the same conclusion that "All...
  18. STEMucator

    Quick Logic Questions Homework: Reduce & Simplify

    Homework Statement 1. Reduce the following logical expression to four literals and draw a gate level circuit, which implements the result. $$AB + BCD + BC + A \bar C$$ 2. Simplify the following: $$(A + \bar B C)(B + C)(B + \bar C)$$ Homework EquationsThe Attempt at a Solution I would just...
  19. Porthos

    Which is more useful for a physics degree: logic or proofs?

    I know that I have already posted a couple of threads like this one (albeit dealing with different courses), but I have had excellent responses here, and I was hoping I could get a couple more. I know that it is best to speak to academic advisors and professors, but there are only a couple that...
  20. Chris L T521

    MHB What are the implications of studying logic?

    Hello everyone, I have a question that seems simple at first but is "hard" for me to answer. I'm teaching a general education math course at a community college next semester, and one of the key components to that course is symbolic logic. I'm pretty confident in my knowledge and ability to...
  21. D

    Logic Gates (NAND to AND Gates)

    couldnt understand why the input is ( (XY)' (XY)' ) ' , IMO , it should be ((XY)' ) ' . because the 2nd logic gates receive (XY)' input from the first logic gates , and the second logic gates act as inverter for the first logic gates.
  22. S

    Math Elective Help: Abstract Algebra, Theory of Numbers, or Symbolic Logic?

    Hello, I'm debating between taking either abstract algebra, theory of numbers, or intermediate symbolic logic as a math elective. Does anyone have any idea which would make my life easier?
  23. J

    How does ladder logic apply to programable logic control

    do any of you know how it would apply ?
  24. H

    Mastering Logical Equivalence Proofs: (P<->Q) ⊣ ⊢ ~(P<->~Q)

    ~(P<->Q) ⊣ ⊢ (P<->~Q) I'm suppose to write the proof for this equivalence but I can't figure it in either direction The closest I got was (P->~Q) from ~(P<->Q) but I can't figure anything else out
  25. H

    MHB Math Logic: Equivalency, Validity, and Consequence

    i take introduction math logic course in college and professor ask for relation between equivalent and valdity and consequence can u help??
  26. H

    MHB What is the meaning of consequence in logic?

    what is the defintion of consequence in logic
  27. H

    Buoyant Force, How's my logic?

    Homework Statement A recreational (open) hot air balloon (i.e., Pinside is approximately Poutside) has a volume of 2107 m3 when fully inflated. The total weight of the balloon, basket, ballast and pilot is 1832.6 N (412 lbs). By how much must the density of the air in the balloon be smaller...
  28. R

    What happens when you tell the dragons about their eye color?

    You visit a remote desert island inhabited by one hundred very friendly dragons, all of whom have green eyes. They haven't seen a human for many centuries and are very excited about your visit. They show you around their island and tell you all about their dragon way of life (dragons can talk...
  29. M

    How to tune the PID parameters using Fuzzy Logic?

    I previously used the Ziegler method to tune the parameters of my PID controller to control my robot's position. I then implemented fuzzy logic for self-tuning the parameters. I have two inputs to the fuzzy logic controller; one is the position error and the error rate. I know that my problem...
  30. V

    PN Junctions vs Transistors When Building Logic Gates

    Is there any reason why logic gates are built using transistors instead of PN junctions? Wouldn't it be more cost-efficient to use PN junctions? I am referring to CMOS logic gates. Also, what can a transistor do that a PN junction can't?
  31. B

    How Can You Simplify Boolean Expressions Using Only NOR Gates?

    Homework Statement Hi everyone, i am currently struggling in my digital design and logic class that includes boolean simplifications and whatnot. I seem to understand how to simplify and am able to comprehend how the karnaugh maps work but what i do not understand is for example, on our...
  32. T

    Topology or logic or other start point?

    So i just recently had to drop two math courses, topology, math logic, because my math maturity wasn't up to the level needed to excel in them. I intend on taking them again, but not without first more preparation which leads to my question. Which order would i benefit more from in preparing for...
  33. emanoelvianna

    Natural deduction sets (Rules of nature deduction)

    Hello fine. I'm studying logic and great difficulties to understand its principles, and should prove some theories involving the laws of identity of sets of mathematics using the method of natural deduction, they are: a) A ∪ ∅ = A b) A ∩ ∅ = ∅ I am trying as follows, but I can not solve...
  34. BondKing

    Can someone please check my logic proof?

    (c v ~ h) - > ~ m (prem 1) T -> ~ c (prem 2) T ^ h (prem 3) trying to get m 1) T (spec prem 3) 2) ~ c ( M.PON prem 2, 1) 3) ~ h (ELIM prem 1 (c v ~ h), 2) 4) ~ h - > ~ m (replace (c v ~ h) with ~h) 5) m -> h (Contrap. 4) 6) ~m v h (M.TOL 5,3) 6) m
  35. A

    Digital Electronics- logic gates problem

    A bulb in a staircase has two switches , one at the ground floor and the other one at the first floor. The bulb can be turn ON and also OFF by any of the two switches irrespective of the state of the other switches, then what is the logic of switching of the bulbs
  36. Y

    How Does a Vernier Caliper Determine Precise Measurements?

    I have made measurements using Vernier Calipers. What I don't understand about them is the coinciding thing. How does one know the value of the last digit of the measurement by seeing which marker of the main scale coincides with the Vernier scale?
  37. N

    Exploring Logic: Finding Answers to Your Questions

    Hey Guys, I am currently a first year computer science student and I am taking discrete mathematics. After having done the logic portion of discrete, I wanted to learn more about logic so I went online and found Peter Smith's guide on learning logic. I followed his advice under "baby-logic" and...
  38. I

    MHB What are the practical uses of logic gates in computing and electronics?

    what are some applications of logic gates? (NOT, AND, OR, NAND, NOR, XOR) also what is a binary selective mask
  39. reddvoid

    Capacitances in NAND2 depletion mode nmos logic

    Why we are not writing Cgs Cdb in depletion mode nmos here why no Csb in bottom nmos Can somebody please explain how to write which components of Cload or provide some links from where i can understand it better thank you, this picture is from...
  40. T

    Question Regarding IC pin numbering and logic gates

    Homework Statement http://i.imgur.com/k8nq4HZ.jpg So I need to assign IC pin numbers to the input and output of the logic gates.Homework Equations None The Attempt at a Solution I only have limited knowledge on integrated circuits as a whole, so I'm pretty confused altogether. I know that I...
  41. V

    Logic behind the Lifting Water problem

    Homework Statement I am trying to understand the logic behind the water pump that requires a user to take into consideration the volume of water at sub-intervals of depth of a tank. There are two types of problems, one where the volume changes at different depths, and one where it doesn't. In...
  42. N

    Need help on logic problem for Biology class

    Homework Statement Hey guys, so I have been trying for the longest time to find the pattern in a hard-level logic problem with no success. I was wondering if someone on here could take a look at the problem and come up with the correct pattern. The variables involved in the problem are the...
  43. K

    Need help with a logic gate circuit please?

    Hello, I just joined because I am having a serious issue figuring out a logic gate circuit with 4 source signals, and a non active state and two items that activate depending on a number of different states for each signal. I've been giving myself a headache for hours trying to puzzle this out...
  44. H

    Logic- How to show something is NOT provable?

    Homework Statement Let S be the theory with no NONlogical symbols and no NONlogical axioms. Show that ~~(x = x) V ~(x = x) is a theorem of S NOT provable without propositional axioms. Homework Equations Let ƒ be a mapping from the set of formulas to the set of truth values such that...
  45. G

    EV and Decision Making: How Utility Functions Impact Our Choices

    So, I'm having a pretty lazy day and decided to do some thinking. And, while this usually turns out to be a splendid idea, today it resulted in me hurting myself. Psychically. So yeah. I've been through a lot of toy games trying to figure out a way to reconcile this all in my brain box, but...
  46. A

    Unifying Numerical Math and Symbolic Logic: Has Progress Been Made?

    In the late 1980's I asked my logic professor if there was some kind of logical and/or mathematical process which unified numerically based mathematics with true-false based symbolic logic.He told me that someone had written a lengthy book which apparently proved that it was totally impossible...
  47. M

    Trying to explain fuzzy logic to a friend.

    Hi, I'm trying to come up with a way to explain fuzzy logic to a friend of mine. After reading this paper: http://www.polytech.univ-savoie.fr/fileadmin/polytech_autres_sites/sites/listic/busefal/Papers/67.zip/67_02.pdf He is adamant that Fuzzy Logic determines the chance that a bit in a...
  48. A

    The algebraic analysis of logic

    Boolean Algebra is a well known field of study in mathematical logic. In Boolean Algebra (BA), a statement can be represented by a variable; usually p, q, r, etc. Under BA each variable can have the value of either 1 or 0; i.e. the domain is the field of integers mod 2. There are many...
  49. K

    Does discrete logic equation ignore death rate during off season?

    Observation of the growth of some beetle population suggests that discrete logistic equation would be more appropriate since these animals have distinct breeding season. discrete logistic equation: Xn+1=Xn+rXn(1-(X2/K)) the result of this equation accounts for population only season to...
  50. P

    Arguments in sentential logic and contradictions/tautologies.

    From what I understand, and please correct me if I'm wrong: An "Argument" in sentential logic is a set of propositions, or premises, which logically lead to a conclusion. I took this definition from http://en.wikipedia.org/wiki/Propositional_calculus However, in my text that I am currently...
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