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. G

    Why in first order logic theories are not possible a demonstration with infinite steps?

    Why in first order logic theories are not possible a demonstration with infinite steps?
  2. icystrike

    Solve "Logic" Questions: Is Jed Right?

    Homework Statement Asked at a press conference whether the new signing, Petermass, would be playing in the big match on Saturday, the Manager replied: “Only if Fredericks isn’t fit.” Three of the journalists present noted the announcement as follows: Jed wrote: “If Fredericks is fit Petermass...
  3. R

    What is the output of a logic gate when one input is not connected?

    Hello, I'm currently studying a course in digital logic. The course is included in my IT program. And I have not taken a course in electronics yet; I will later. My question basically is: what is the output of a logic gate given that one input is neither connected to a high voltage nor...
  4. V

    Something I discovered doing logic

    I haven't known about a law that says so. Step 1: using two numbers in any format: binary, octa, hexa, do an AND operation. Step 2: Perform OR operation on the same numbers. Step 3: Add the results of step 1 and 2 numerically. The result comes out to be the same as the sum of original numbers.
  5. M

    How to use Logic gate in Breadboard circuit?

    I am a High school student, I have read about Logic gates but when it comes to practical use I am confused. I am building a small project where I want to use OR and AND gate, but I don't know In which form they are available in the market, how to connect them on breadboard and how to power them...
  6. Blargian

    Dimensional Analysis in Halliday/Resnick

    Hello world! I'm busy working through Halliday/Resnick Fundamentals of Physics chapter 1 and I'm having some difficulty with this particular question. I'll do my best to explain my reasoning and attempt at the problem 1. Homework Statement The problem: Three different clocks A, B and C run at...
  7. M

    MHB Logic Book: Definitions, Language & Existential Formulas

    Hey! :o Could you suggest a book of logic that contains definitions, like the definition of a language, of an (positive) existential formula, etc?
  8. W

    What Is the Probability of Distributing Spades Among Players in a Card Game?

    Homework Statement If you have a 52card deck and split it evenly to 4 people (a,b,c,d) then what is the probability that persons a and b have 7 spades and person c has 3 spades. Homework Equations P(A) = |A|/|S| The Attempt at a Solution I divided up the decks 4 ways. So Persons a and b...
  9. kostoglotov

    Proving dependent columns when the rows are dependent

    I feel like I almost understand the solution I've come up with, but a step in the logic is missing. I'll post the question and my solution in LaTeX form. Paraphrasing of text question below in LaTeX. Text question can be seen in its entirety via this imgur link: http://i.imgur.com/41fvDRN.jpg...
  10. Willelm

    Can you solve the hardest logic problem?

    Maybe you know that that problem was about 3 gods. 1 tells the truth, other always lie, and the last god gives a random answer. The gods can only answer a yes/no question. Can you tell what god lies, tell the truth or give a random answer with only 2 And ONLY 2 questions? Harder than it was, of...
  11. A

    What's the logic behind partial fraction decomposition?

    Ok so I took partial fraction decomposition in Calc II, and now I'm taking it again in Differential Equations course. The problem is that I don't really understand what I'm doing. I understand the procedure when having simple real roots, for example 2x+1/(x+1)(x+2), it becomes A/(x+1) + B/(x+2)...
  12. SmokeyMTNJim

    Logic, Truth Table question

    << Mentor Note -- Moved from the technical math forums, so no HH Template is shown >> I am currently working through a Finite math book Intro to finite math: second Edition Kemeny, Snell, and Thompson. One of the exercises wants me to construct a truth table for the following: ~(p|q)...
  13. P

    How to Prove (∀x)(A→B) ≡ ((∃x)A) → B Using First-Order Logic

    Hello, I am having particular trouble with the below problem. We are using http://studygig.com/uploads/materials/math1090_mathematical_logi.pdf and we must prove this statement using Hilbert style or Equational style proof (first-order logic), but any proof of any type would point me in the...
  14. Strilanc

    Delayed choice as a quantum logic circuit

    The recent thread about the delayed choice experiment made me want to understand the experiment as a quantum circuit. I made this: (contrast with http://www.nature.com/nphys/journal/v8/n6/images/nphys2294-f2.jpg) The left hand side is the qubit-holding wires and gates to apply, with Alice...
  15. Raman Choudhary

    Logic behind definition of Reparametrization

    What is the intuitive logic behind setting up the definition of reparametrization as being a bijective map and all that(the inverse map being smooth) and not alone that the reparametrisation must give us the same image curve.e.g if we see (t,t^2) as being describing the same curve as (t^3,t^6)...
  16. SrVishi

    Expansive Mathematical Logic Text

    Hello, I want to start learning mathematical logic. I was wondering what would be a good "expansive" mathematical logic book that covers as much material as possible. My school has books by both Ebinghaus (et. al) and Monk. Are these good? I've heard good things about Schoenfield, but I was...
  17. hellsteiger

    Books on Quantum Logic and Computation

    Hey there PF'ers. I'm looking for a nifty book or site on Quantum logic and Computation. The sort of book like that would cover digital logic - jumps over all the explanations of underlying working and goes straight to logic and computation. I know it's important, but I have done courses in...
  18. agent1594

    Symbolize propositions using predicate logic

    Homework Statement Suppose that predicates and individuals are dened as follows: S: should be shunned, U: is prone to unruly behaviour, P: is a friend of Peter's, M: is a friend of mine, a: Ann, d: David. Symbolize the following: i. Ann is a friend of Peter's and David is a friend of mine...
  19. jk22

    XOR or OR: Examining Everyday Logic

    In logic a or b is true if both a and b are true but do you think the everyday or is in fact xor ?
  20. V

    Computer/processor logic design textbook recommendations?

    Looking for a solid introductory text on computer logic with emphasize on hardware design. There is tons of material out there, but it seems to me most of them are oriented towards low level software design, rather then hardware design: lots of register transfer codes, VHDL/Verilog simulations...
  21. Carnal

    What is the next shape in the series?

    I've been staring at this for hours but I do not get how the pattern works at all. The problem is from this website. It's not that I'm an idiot, I think there's something wrong with the pattern!
  22. kostoglotov

    Line Integral/Ampere's Law: is my logic valid?

    This is a problem from a section on Line Integrals in my Calculus Textbook, I haven't studied any physics relating to E&M yet, and the solutions manual only gives solutions for odd numbered problems. Sorry, if I'm posting in the wrong forum, I hope I'm not. 1. Homework Statement A steady...
  23. A

    Solving Sudoku: A Logical Approach

    How to solve the attached Sudoku without computer or a guess?
  24. marabou_2015

    A question on Beth's semantic tableaux

    I have two questions to ask: (a) Is there some rule for estimating the number of branches in a Beth tableaux in advance? and (2) is the number of the open branches in a semantic tableau equal to the number of the interpretations that assign to the propositional type a true value? If the answer...
  25. EverGreen1231

    Logic diagrams for relays help

    Good morning, I'm looking at some logic diagrams for relays and have encountered something that I've never seen before. I haven't looked on the internet extensively since I thought the folks here at the forums would be able to answer my question more quickly. My experience with logic is...
  26. S

    MHB Logic Puzzle: Where is the koala?

    Anyone like riddles? I've got funny one. ​The Math Riddle Question: Where is the koala? There are five houses, each of a different color and inhabited by men from different territories, with one unique animal*, drink, and car. Some facts are given: 1. The Tasmanian lives in the red house. 2...
  27. ichabodgrant

    Op-amp as a comparator (analog-to-digital conversion)

    Homework Statement Okay, This time it's an exam question. I am doing some past papers and there are questions about comparators which are not introduced in this course (this course is preliminary course for engineering students who are interested in electrical, electronic or computer...
  28. S

    MHB Logic equivalence and implication, question

    Hey guys I am having a bit of a difficult time with this question, if some one could help me out it would be appreciated, thanks. Consider the following argument. "If the weather is fine, and the train is early, then the dog will sit on the tuckerbox. The train will be early, (but) also there...
  29. S

    Why Does Placing 26 Points in a 15x20 Rectangle Guarantee Close Proximity?

    <<Mentor note: Missing template due to originally being posted in other forum.>> So, my professor gave a problem which stated: Given a 15 x 20 rectangle, prove that if 26 points are chosen, at least one pair will be at most five units away. What I said was to split the rectangle into 12 5x5...
  30. nomadreid

    Fuzzy logic and the Liar paradox

    I have once again (this time in http://www.economist.com/node/2099851) come across the argument that a fuzzy logic solves the liar paradox by assigning the liar sentence a truth value N, other than T or F, with [[A]] = N ⇒[[~A]] = N. However, I don't see that this gets around the essential...
  31. nomadreid

    What is "meaningful" for a multi-valued logic?

    In theories with a two-valued logic, a sentence is "meaningful" if it is (with respect to a given model) either true or false. Does this definition need to be modified for multi-valued logics? If so, how?
  32. heff001

    Pure Mathematics study - question

    I am planning to study the following pure mathematics areas (on my own) and wanted to know if this is the best sequence: 1- Formal Logic 2 -Philosophical Logic 3- Sentential Logic 4- Predicate Logic 5- Symbolic Logic 6 -Set Theory 7 -Pure Mathematics (Intro, Pure Math I and II and Hardy) -...
  33. F

    Create a logic circut with encoder in multisim (adder/subtractor)

    hello how can i use full adder with encoder in multisim to add and Subtract two decimal number and create it
  34. D

    Engineering Eq. Logic Expression for Circuit 2

    Homework Statement https://www.dropbox.com/s/d3qdr96n27j8wa7/circuit.png?dl=0 The questions is as follows: For each circuit write the equivalent logic expression. Homework Equations (B' + C) * A (?) My Attempt at circuit 2 (A* (A' * C') * B') + (A * C * B) My Attempt at Circuit 1 The Attempt...
  35. G

    MHB Logic Circuits and Truth Tables

    Hey guys, I'm in a pickle with this question. Its really not my cup of tea, its a struggle factor really but I don't really have a choice whether I like it or not. A worked example such as this allows me to see what it is I need to do. If anyone can provide a helping hand it would assist me...
  36. xconwing

    NOT logic at transistor/componet level

    Hello all, Reading this article http://www.allaboutcircuits.com/vol_4/chpt_3/2.html explaining NOT logic at component level. I'm not sure I understanding the arrow drawn in this figure: above sentence "This tells us that ..." Is the arrow depicted current? If so, would that make passing the...
  37. Vinay080

    Logical/mathematical proof for the identity of electron

    Premise 1: Physics don't believe in sense "organs" of the human "robot" (more commonly said "common sense deceives us"). Premise 2: Physics believes in logic or mathematics. Background thrust: Quantum mechanics. Premise 3: Everything which "revolves" around the nucleus might not have...
  38. E

    Question on the Logic of the Monty Hall Problem

    Consider this example: A player in a game show was asked to choose between three doors, two doors contain a faulty prize, while the other contains a million dollars. As the player wanted the money, he chose one (in this case, the probability of choosing the door with the money is 33.33%). Since...
  39. M

    Help with decoders and RAM [Digital Logic]

    First I really don't know where I should post this (I'm assuming this place is fine, maybe coursework?) So I built a circuit that includes a 1k x 4 RAM ( so I'm assuming that stands for 4000 Kb but I wouldn't see why you'd need to write 1k x 4 RAM) Furthermore, I'm having trouble...
  40. Byeonggon Lee

    Good and easy mathematical logic book for computer science

    Hello I recently noticed that mathematical logic is related to computer science. I haven't studied math in university yet I'm not good at math and Since I'm not a native English speaker some English is hard to me. Is there any good and easy book which describes mathematical logic used in...
  41. Byeonggon Lee

    Proof of (p ⇒ q) =(¬p ∨ q) in Mathematical Logic

    Hi :smile: I am studying mathematical logic by a pdf file. But there is no proof about this therorem so I don't understand.. How to prove this?
  42. L

    Force, Horsepower and Acceleration logic?

    hi guys, Im not a science student but wanted help in understanding a few fundamentals. Here is where i have learned till please correct me if i am wrong. is it correct if i state, "If you can lift 74.6kgs off the ground to a height of 1m in 1sec you have power = 1hp?" i say that cause i read...
  43. STEMucator

    Fixing hazards in a logic expression

    Homework Statement Identify and fix all hazards in ##f = (ab + \bar{a}c)(c + \bar{b}) + ab##. Re-check if the final expression obtained is hazard free. Homework EquationsThe Attempt at a Solution So I used a binary tree and found a static 1 hazard present for ##bc = 11##. The hazard was ##a...
  44. B

    Suggest one way of sizing the transistors of the logic

    Homework Statement Suggest one way of sizing the transistors of the logic circuit such that its worst case tpHL equals the tpHL of an inverter with a sizing of (W/L)min. Homework Equations I think the only equation is the (W/L) itself. The Attempt at a Solution I have actually done the front...
  45. LAZYANGEL

    3 barrel question / logic puzzle

    First of all, this is NOT a homework question. So I give you three barrels, one has 50 apples, the second has 50 oranges, the third has 50 - a mixture of both apples and oranges. However, I have intentionally placed the wrong labels on all of them. Find the minimum number of fruits you need...
  46. N

    Translating quantificational logic

    Homework Statement Put the sentence into symbols using the suggested notation. Dolphins and porpoises grin and frolic in the sea. (Dx = x is a dolphin; Px = x is a porpoise; Gx = x grins; Fx = x frolics in the sea) Homework Equations None. The Attempt at a Solution [/B] (\forall...
  47. U

    Convert sentences into First Order Logic

    (1) Anyone who is thin, tall and energetic will be good basketball player. (2) Some people are tall but not good basketball players. (3) Anyone who do exercise or eating healthy food will be energetic. (4) Saman is thin and tall person who do exercises. Write the above sentences in First Order...
  48. RaulTheUCSCSlug

    Using Arduino as a Logic Switch

    I want to supply some LED's and a motor from an outside source of electricity (i.e. a battery pack, wall outlet, batteries in series, etc.) and want to use the Arduino to be able to "switch" on and off these sources so that I am able to control long strands of LED's with the Arduino (for like a...
  49. A

    Design of Basic All-NAND Circuits using Logic Gate Technology

    The problem statement Hi I'm writing a report on a design of a basic all-NAND circuit. In reality, how are these circuits made ? Do we just use TTL etc. integrated circuits and combine them as necessary? Thanks
  50. 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...
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