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.

View More On Wikipedia.org
Recent contents Top users
  1. K

    Are These Logic Problems Valid or Invalid? A Scientific Analysis

    Hi people, I'm trying to solve a logic problem but I'm having some issues with a couple of them. I appreciate if you can help me with it. 1.- (∀x) (∃y) (x=y) 2.- (∃x) P(x)→(∀y)P(y) Demostrate if valid or invalid each one. Thank you!
  2. D

    Solving First-Order Logic Problem with Valuation Existence

    I have a problem I can't quite figure out: I have a first order system S, and an interpretation I of S. I have to show that a closed well formed formula B is true in I if and only if there exists a valuation in I which satisfies B. I've done one of the two implications, but I still have...
  3. M

    Proof that Sqrt[3] is irrational - Is my logic valid?

    I am self-studying elementary analysis and am learning how to prove things. I have come up with a proof that √3 is irrational, and I believe it is valid, but I am unsure of my logic, as I have not seen it proved in just this way, and I don't have a prof to ask! So if anyone could just take a...
  4. L

    Should I change my major?Mechanics & Logic: Issues Changing Majors?

    Hi everyone! I'm having a problem. I would really appreciate some answers. I'm thinking of changing to another major. :\ I'm majoring in Industrial Eng., which has a lot of mechanical classes at my institute. I have a very logical mind, and I like to connect everything about a subject: from...
  5. M

    How is uncountability characterized in second order logic?

    How is uncountability characterized in second order logic?
  6. S

    Losing Contact With Logic: Examining the Thin Layer of Reason

    When ever I go trying to solve a problem, especially the ones that have my mind greatly diverge into many concepts, I seem to notice myself losing contact with logic. Its like a bad dream really. I find myself attempting to solve how I am solving a problem and so on. Or at least questioning what...
  7. N

    A hard differential equation - where is the error in my logic?

    [SOLVED] A hard differential equation - where is the error in my logic? Homework Statement 2xyy' + y2, where y is a function of x The Attempt at a Solution 2xyy' + y2 = 12x2 |*(1/x) => (y2)' + y2/x =12x |*ln(x), 2yy' = (y2)' => (y2ln(x))' = 12x*ln(x) => y2ln(x) = ∫12x*ln(x) =>...
  8. E

    Engineering Understanding Voltage Distribution in an Electrical Circuit Logic

    Trying to study in preparation for an exam, I've been told that I need to consider the circuits a little more. So in this circuit: Would the voltage across the resistor be the voltage across V0? Or would it be the voltage across the inductor because the capacitor is keeping the resistor...
  9. F

    Good Mathematical Logic Textbook?

    I've been trying to decide on a mathematical logic textbook to teach myself a bit. I'm taking a course on it next semester, but I have never had a logic course before (I've had some CS courses though and proof-y math courses). I'm also taking a modal logic course the semester after math logic...
  10. M

    Logic puzzle solution without guesswork?

    Here's the puzzle: http://9gag.com/gag/4137344 Now, I did this fairly quickly with the right tools(another use for excel found). However along the way I had to make 2 assumptions/random guesses: The yellow vs dunhill in houses 1 or 3 The dane vs tea in houses 2 or 5 Question being, can this...
  11. R

    MAking logic gates with 3-pin trasnistors

    I'm trying to make logic gates using MOSFET transistors, for a lab. for the prep, my lab group designed logic gates based on 4-pin transistors, but the MOSFETs we were provided with only have 3 pins. Is it possible to make logic gates using 3-pin trasnistors, and if so how?
  12. R

    Programs EE Majors: Should I take Electric Circuits or Digital Logic?

    I'll be taking a heavy workload of classes next semester. This will be the first time I'll be taking all technical classes. To ease my transition, should I take electric circuits or digital logic? What is the general consensus in terms of which one of these classes is more difficult?
  13. D

    Incredibly simple question about the logic behind systems of equations

    I know this is a simple question but I can't exactly figure out the logic governing this problem, I just know it had to be this way. Let's say I have two equations: x - 4y + 9 = 0 y - 3x + 5 = 0 If I set them equal to each other then I get no where because I'll have both x and y in the...
  14. binbagsss

    Quick logic question,SHM, second order differential equation

    See attached diagram. Taking downward as postive. The particle is pulled down past its equiliburm position (e=l) by l/2 and then released. It has mass m and is subject to a resistive force R. Why is it that the equation is mg - T - R = ma [1] as a pose to mg - T + R = ma.[2] I...
  15. H

    How do physicists use redshift to determine the expansion of the universe?

    by measuring redshift physicist conclude 1.most of the galaxies are moving away from our galaxy 2.universe is expanding 1.most of the galaxies are moving away from our galaxy if we ride alongside a train on a motorbike with relatively same speed , do we don't hear the doppler effect ...
  16. H

    Proving \neg x \vee x in Hilbert System: A Logical Dilemma

    Homework Statement Prove \neg x \vee x using Hilbert system. Homework Equations The logical axioms. I'm not sure if I should state them, or whether there is a standard set. It seems to me that different sets are used. Anyway, the ones with disjunction in them are: a \rightarrow a \vee b...
  17. X

    Making a Logic Circuit: Learn How to Build an OR Gate

    Hello all, I recently started working with circuits and in my classes I learned and used some logic circuits. It was pretty cool but we never actually went over what makes up an IC of one of the logic components. I really want to know what goes on inside the IC, so I was wondering, how...
  18. A

    Meaning of this statement (logic)

    This is from Velleman's 'How To Prove It' book (not homework! Reading through it myself) Let S stand for the statement 'Steve is happy' and G for 'George is happy'. What English sentences are represented by the following: a) [S ⋁ (G ⋀ ¬S)] ⋁ ¬G I interpret it as saying 'either Steve is...
  19. A

    Intro to Logic: Constructing Proofs

    Hey, I'm new to the forum so I'm not sure if I posted this in the right section. I'm taking Intro to Logic and I'm having some problems. Proofs: Construct proofs for each of the following symbolic arguments. Commas are used to mark the breaks between premises. (Each proof can be completed in...
  20. J

    Newton's logic behind taking force as change in momentum w.r.t time?

    why Newton had taken force as change in momentum per time? i mean i need to get physical interpretation?what is this force actually? also help me to get an idea about energy in sense(core concept)? not with some equations? i see these equations every time?but didn't know meanining? somebody...
  21. Rasalhague

    Uncovering the Logic Behind Cl(A) = A

    Cl(A) = A' ?? Unraveling the definitions, I keep getting that Cl(A) = A'. x\in \overline{A} \Leftrightarrow (\forall U\in \tau)[(A\subseteq X\setminus U)\Rightarrow (x\in X\setminus U)] \Leftrightarrow (\forall U\in \tau)[\neg (x\in X\setminus U)\Rightarrow \neg(A\subseteq X\setminus U) ]...
  22. D

    Sequential Logic Design-State Diagram for a divider

    Sequential Logic Design--State Diagram for a divider I need to design a divider so that when input C=0 it divides by 3 and when input C=1 it divides by 4 and I need to use D,T,and JK flip flops (I'm not even sure I'm phrasing this correctly). I'm just having trouble with a few concepts. I'm...
  23. N

    CMOS gate for the logic function

    Hello. One of my friends told me that the logic function for (A.or.B).and.(C.or.D) is From a book, I know the P1, P2 , N1, N2 form a NAND. The same for P3, P4, N3, N4. And P5, P6, N5, N6 form a NOR. My question is, is this circuit the same as (A.or.B).and.(C.or.D) ? Thank you
  24. J

    Find the gain in a non-ideal op amp - check my logic

    To start I have attached an image of the circuit. We are to relate the V_{0}to V_{s}. I am not exactly sure where to start with it. I know that V_{-} and the V_{+} on the op amp have to have the same voltage. The resistor that bridges the two inputs is throwing me off. Not sure if this is the...
  25. B

    Abstract math, sets and logic proof

    Homework Statement If A is a set that contains a finite number of elements, we say A is a finite set. If A is a finite set, we write |A| to denote the number of elements in the set A. We also write |B| < ∞ to indicate that B is a finite set. Denote the sets X and Y by X = {T : T is a proper...
  26. R

    Sentential logic exercise from 'How to Prove it - A Structured Approach'

    Homework Statement This is an exercise from 'How to Prove it - A Structured Approach' (Exercise 7a, page 54) . So far a a really great book. Homework Equations The DeMorgan, Absorption, Idempotent, Double Negation, Commutative, Associative, Distributive, Tautology, Contradiction...
  27. N

    Questions about the logic of infinity

    I asked a question related to infinity a few weeks ago, but the answer I got really lead me to a confusion. Is there any way, that infinity can be compared in another plane or whatever. So here is something paradox if you treat infinity as it is in the set of real numbers...
  28. L

    Help with indirect logic proof please

    Using the five axioms below prove: p→q A1: p→~y A2: ~r→q A3: p→~z A4: x→ q or z A5: r→x or y Do I have to take the contrapositive of some of the axioms to begin this proof?
  29. L

    Help with indirect logic proof please

    Using the five axioms below prove: p→q A1: p→~y A2: ~r→q A3: p→~z A4: x→ q or z A5: r→x or y Do I have to take the contrapositive of some of the axioms to begin this proof?
  30. Femme_physics

    Statics Mechanics: Looking for the flaw in my logic

    Yep...back to old statics. Not because I have a test (already passed it in flying colours) just for fun seeing what I can solve and can't...now I ran into this:Homework Statement http://img705.imageshack.us/img705/1533/pulleyf.jpg Statics: The weight is 50kg. Find force P to hold it in...
  31. G

    Max/Min in Calc III- Confused about relation between equations logic?

    So, I technically got this problem correct (our professor gave us the answers but not the total solution). My question is more of a logic one- an answer that I'll need to apply this concept to problems on the exam. I included it at the bottom of the post, after I explained the problem Find...
  32. F

    [LOGIC] Prove if y + (-x) = 0 then y = x

    y + (-x) = 0 → y = x Need to do this in Tarski arithmetic, axioms below, as well as results below that which have been previously proved I really have no idea how I can move this x over, can anyone help me out with a starting axiom? Is it just TA4 that implies y=x? That simple? If it is...
  33. F

    [LOGIC] Proof by Induction in Peano Arithmetic

    I have to do the following using these axioms PA1-7, the others below it are previously proved results I can use too. [Sa] means the successor of a. Base Case: y = S0 x.S0 = S0 → x.0 + x = S0 → 0 + x = S0 → x = S0 & y=S0 Now the induction step is usually y=a to y=Sa, however this does...
  34. P

    Help me parse the logic of this statement

    So I have this statement that I'm supposed to prove and I cannot for the life of me figure out what parts I'm allowed to assume and what part I am expected to prove, here it is:The residue of an analytic function f at a singularity a ∈ ℂ is the uniquely determined complex number c, such that the...
  35. Femme_physics

    How to Draw Logic Gate Graphs for NOR and XOR Gates

    Homework Statement Graphs A and B are entries to a NOR gate with 2 inputs. Draw the output C. Graphs X and are entries to a XOR gate. Draw the output Z. Homework Equations The Attempt at a Solution
  36. E

    3 Input Majority Logic Circuit

    I want to implement a three input majority logic (when at least two of its inputs are 1, the output will be logic 1) by using only 2-input NAND gates. It is required to find the most simple one, with the lowest number of NAND gates, I could construct one with 6 NAND gates, but does anybody know...
  37. B

    How does a logic gate permanently maintain its state?

    Logic gates can be switched to a high state, where the current flow is cutoff and a low state, allowing current to flow through. What electromagnetic processes in the semiconductor material enable this to happen? Since the switching action is purely electronic and there are no moving parts...
  38. C

    Are \alpha and \beta logically equivalent if ~\alpha and ~\beta are?

    Be \alpha and \beta two formulas of the propositional calculus, show that \alpha and \beta are logically equivalent if and only if ~\alpha and ~\beta are logically equivalent.
  39. S

    Modern Classic Logic: A Comprehensive Guide to the Laws of Thought and Truth

    A Modern Interpretation of Classic Logic Basic definitions. Definition of Truth: "x" is true if and only if x. Laws of Classic Logic: Law of identity: x = x Law of contradiction: Nothing is both true and not true. Law of excluded middle: Everything is either true or not true. Im...
  40. A

    Engineering Differences between Logic Function and Logic Circuit

    Homework Statement The task required me to find the logic function / circuit for : a. comparator b. multiplexer c. adder d. register e. shifter So what are the differences between logic function and logic circuit? Thank you :) Homework Equations The Attempt at a Solution
  41. G

    Discrete Math Logic Defineing a function recursion-ish

    (3) De fine a function A(m,n) as follows. A(0,n) = 2n for every n. A(m,0) = 0 for every m >= 1 A(m,n) = 2 if m >= 1 and n = 1 A(m,n) = A(m -1,A(m, n - 1)) otherwise (i.e., if m >= 1 and n >= 2. (b) Prove A(m,2) = 4 for every m >= 2 (c) Prove A(1, n) = 2^n for every n >= 1. Proving...
  42. T

    Geometry, logic and sun angles: help

    I am trying to figure out what size eaves we need for our house extension. I've tried a few calculations and now I'm posting here in the hope that a logical thinker will be able to tell me what I'm doing wrong. We live in Adelaide, Australia, and we want to put in glass double-doors on a...
  43. T

    Muons experiment, strange logic

    In the muons experiment the flow is measured at top of a mountain and at the base of the mountain. The velocity of the muons was calculated http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muonex.html The velocity is 5 times the speed of light, which is of course against the relativity...
  44. H

    MHB Best Logic Textbooks for Advanced Learning

    I was wondering if anyone could recommend some good logic textbooks. I have done introductory courses covering, propositional and predicate logic (with natural deduction, semantic tableaux, axiomatic systems...) covering the completeness, soundness and compactness results (amongst other things)...
  45. D

    Relativity: what's wrong with this logic?

    Okay, suppose we know that the laws of physics are invariant with respect to a shift in position, and invariant wrt a shift in time (ie the transformations \mathbf{r}\ \rightarrow\ \mathbf{r}+\delta\mathbf{r}\ \mathrm{and}\ t\ \rightarrow\ t+\delta t preserve the laws of physics). Then wouldn't...
  46. P

    Proving Statements by Contradiction: Understanding the Logic Behind It

    Hi, I have a question about proofs by contradiction in general. Without getting into the mathematical details, suppose we had the statement: For every (condition A), B is true. If we want to prove this by contradiction, we want to assume the negation of this statement, and then prove it to...
  47. J

    Logic of quantified statements: for all vs if then

    Statement 1: If n is any prime number > 2, then n+1 is even. Statement 2: For all prime numbers p, if p>2, then p is even. The above two statements seam equivalent, but have different converses, etc. converse 1: If n+1 is even, then n is a prime number > 2. converse 2: For all prime...
  48. Saladsamurai

    Sentential Logic: Is the argument valid?

    Homework Statement I am going over the first chapter of Velleman's How to Prove It. I have never studied logic before and while I understand most of what is happening, I am not sure that I am understanding how to transform sentences into symbols that can be tested. One of the exercises asks...
  49. Femme_physics

    Logic Gates with XOR gate need to verify solution

    Homework Statement Basically and most importantly... I wanted to see if I got my F function correct. That's at clause 2. At clause 3 I'm told a = b = 1 c = d = 0 and to calculate At clause 4 I'm asked if the logic value of P is 1, if the logic value of Q matters... The...
  50. N

    Difficult Predicate Logic Symbolization

    Homework Statement I do not know if this is the right forum or subforum for this kind of topic. So if it is not, I apologize in advance.Symbolize the following sentence: Given that some mean elf will bite and some friendly one will too, the mean ones will bite whether or not provoked but the...
Back
Top