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. L

    Exploring the Logic Behind CMOS Voltage: 3.3V

    Why is the CMOS logic voltage exactly 3.3V, why not 3V or 3.5V?
  2. O

    The Logic of Elementary Particles

    "In particle physics, an elementary particle or fundamental particle is a particle believed not to have substructure; that is, it is believed not to be made up of smaller particles." -Wikipedia How does someone ever possibly (LOGICALLY) conclude that a particle is not made up of smaller...
  3. Saladsamurai

    How Do BJTs Help Create Logic Gates in Circuits?

    Hello all :smile: I am a mechanical engineering student taking an introductory circuits course. I find the things we are doing in lab quite interesting, but I really lack a good understanding of what we are doing. We are currently building logic gates using BJTs. I have some basic...
  4. K

    First order logic: definability

    Homework Statement What subsets of the real line R are definable in (R,<)? What subsets of the plane RxR are definable in (R,<)? Homework Equations A subset is definable if there is a formula in first order logic that is true only of the elements of that subset. For example, in the...
  5. L

    Logic: Difficulty for Students vs Analysis & Algebra

    Do most students find it more difficult than analysis and abstract algebra?
  6. K

    Unatisfiable union of sets- sentential logic

    Homework Statement Prove that if A and B are two sets of well-formed formulas (logical statements, abv. wff) such that A union B is not satisfiable, then there exists a wff k such that A tautologically implies k and B tautologically implies not k. Homework Equations This question is in...
  7. K

    Sentential logic substitution rule

    Homework Statement Show that if A is a tautology, then so is *(A). A is a well formed formula, * is a function that replaces all sentence symbols A_1, A_2, etc. with formulas B_1, B_2, etc. , respectively Homework Equations * is defined recursively, starting with the fact that if A_n is...
  8. M

    Quick questions about logic gates (Nand, nor, etc)

    So recently just in my spare times I've found an interest in logic gates such as the nand gates and nor gates and such and although most of it's logic, there's one thing i just couldn't figure out. Let's say you have a nand gate configuration consisting of two pmos and two nmos transistors as...
  9. A

    Is Peter's Dislike for the Groom Supported by FOL Rules and GCWA?

    We have the following sentences which I translated them to FOL by using the language: Att(x) for "x attended the ceremony" Likes(x,y) for "x likes y" Rel(x,y) for "x is a relative of y" Ab(x) for "x is an abnormal relative" (a) Only all the normal relatives attended the wedding...
  10. M

    Solve Logic Box Question: Apples, Oranges, Apples & Oranges

    Homework Statement If there were three boxes, one box is made of apples, the other is made of organes, and the last is made of organes and apples. You are able to open only one box without looking in, and you are able to look at only one fruit inside the box. By looking at the fruit, how can...
  11. A

    Solving First Order Logic w/ Huey, Dewey, Louie: Age, Color & Design

    Could anyone help me with this? Donald and Daisy Duck took their nephews, age 4, 5, and 6, on an outing. Each boy wore a tee-shirt with a different design on it and of a different color. You are also given the following information: ■ Huey is younger than the boy in the green tee-shirt. ■...
  12. A

    Resolution in predicate logic

    I need help with the following question on Resolution in FOL. The custom officials searched everyone who entered this country who was not a VIP. Some of the drug pushers entered this country and they were only searched by drug pushers. No drug pushers was a VIP. Let E(x) mean ”x entered...
  13. M

    Uncovering the Logic Behind the Center of Mass Formula

    Homework Statement is there any intuition of why the center of mass formula is what it is? in high school the teacher says is is what it is and that's that or something like that but is there any logic behind it? Homework Equations The Attempt at a Solution
  14. T

    What are some books on set theory that use formal logic?

    I recently learned predicate calculus from Schaum's Outline of Logic. in this sort of form: In addition to refutation trees, however; pfff, refutation trees. I'm reading "Introduction to Set Theory," Hrbacek, Jech. I'm a little "annoyed" by the informal proofs. Are any books that teach...
  15. T

    Is the flow of my logic flawed?

    If two numbers are not equal, there is infinitely many numbers between them. Therefore, numbers that are equal have a finite amount of numbers between them, 0. Therefore, numbers with a finite amount of numbers between them are equal.
  16. P

    Engineering Need a help in making logic circuits

    Homework Statement So I have four bits input(X0,X1,X2,X3), and I need to check if these four bits are monotonic sequence. I got the following function: Y0 = X2X1X0 + X3'X2'X1' + X3'X2'X0 (Y0 - the output 1 when X0>=X1>=X2>=X3) Y1 = X2'X1'X0' + X3X1'X0' + X3X2X1' (Y1 - The output 1...
  17. J

    George boole and boolean logic

    Were computers or any such devises there during George Boole's times who lived through 1815-1864? I don't think there were any such things, then what did motivate or make Boole to invent such a new field? Please help me with this. Thanks.
  18. C

    Help building one flip flop using another? (Digital Logic Design)

    Can anyone show me the proper procedure to construct a flip flop using another flip flop? My Teaching Assistant gave us these steps you can use on any occasion but I cannot seem to apply it in this certain case. How do you build a JK flip flop using a Toggle Flip Flop with an Enable? The...
  19. J

    Logic gates and boolean algebra

    Hi I'm not a science or physics student - quite a layman. Therefore, please keep your replies simple and explanatory so that your guidance and help can be fully appreciated. Thanks. What are these logic gates - AND, NOR, NAND, etc? Are these some physical circuits? In Boolean algebra...
  20. S

    Understanding "If... then..." Logic: Examples and Explanations

    "If... then..." p: I eat breakfast. q: I do not eat lunch. T: true, F: false. If I eat breakfast then I do not eat lunch. p → q is T If I eat breakfast then I eat lunch. p → q is F If I do not eat breakfast then I do not eat lunch. p → q is T If I do not eat breakfast then I eat lunch. p...
  21. K

    Why Does Increasing Sampling Frequency Fix Sequential Logic Simulation Issues?

    [SOLVED] Sequential logic simulation I have built a circuit (using the SystemVue software package) that has a 5 bit adder (adds two 2s-complement five-bit numbers - A4A3A2A1A0 and B4B3B2B1B0) with overflow detection and saturation circuits. I am trying to clock the data in so I can check if it...
  22. C

    Converting 3 Logic Levels to 2 Logic Levels for Laser Driving Systems

    I need help with a mini communication project. I am trying to receive signals from RJ45 Ethernet (10 BASE-T), which comes in three logic levels (-2.5, 0, +2.5) and convert it into two logic levels so I can drive a laser on and off. Would anyone know of any IC's that can accept these signals to...
  23. N

    Understanding the Use of 'Provided That' in Logic

    "Provided that... " My current calculus text uses the words "provided that" a lot, and I'm not sure what those words mean in the context of logic as the use of those two words seems to mean different things depending upon the context... p,q assertions I know that If p, then q is...
  24. H

    Symbolic Logic Homework: Mean & Friendly Elves Bite

    Homework Statement Symbolize this statement: Given that some mean elf will bite and some friendly one will too, the mean ones will bite whether or not provoked but the friendly ones will bite only if provoked. Homework Equations let's say A=for all, E=there exists, & is and, (or) is...
  25. J

    Ox-words: Rules, Length & Occurrences of a & b

    Homework Statement Ox-words are sequences of letters a and b that are constructed according to the following rules: I. The sequence consisting of no letters is an Ox-word. II. If the sequence W is an Ox-word, then the sequence that begins with a, followed by W and ending in b, written aWb...
  26. G

    Logic Design- Transfer Characteristics and Noise Margin

    Hello, I have the following question which I'm not quite sure about. I have the following Transfer Characteristic for a buffer. You can see the graph breaks at the points (2,0),(3.5,4),(5,5) http://img521.imageshack.us/img521/5052/captureen.jpg I need to set the appropriate values...
  27. T

    Solving NAND Boolean Logic Homework w/ Q=A+B+C+D

    Homework Statement Taking the statement Q = A + B + C + D Rewrite using only NAND (2 inp) and NOT gates Homework Equations Well I want to do it all in NAND gates - because we can easily tie NAND inputs to make it a NOT \overline{AA} = \overline{A} The Attempt at a Solution...
  28. R

    Second Order Predicate Logic vs. First Order

    Hey, I'm studying Predicate Logic at the moment and I can't seem to wrap my head around the way that english sentences would convert into second order logic. What kind of sentence can be faithfully represented in PL2 but not in PL1? Sorry if this isn't the appropriate section; I'm actually in...
  29. H

    Find Logic Classes in the US: Course Code & Info

    I would really like to take a logic class, but I can only find philosophy classes that have logic. Have you ever taken a logic class with philosophy? If so, did it cover logic exhaustively? Do you know if there are any classes that have logic solely? If so, what was the course code for that...
  30. L

    How to add a few logic symbols to LyX?

    Homework Statement I think LyX is a great program. However, as a beginner, I am having trouble with adding new symbols. I am taking a Mathematical Logic course as a graduate student, as the assignments get harder and harder, the default mathematics symbols simply don't cut it anymore, so...
  31. L

    Engineering Logic Design - Combinational Circuits

    Homework Statement Implement the following boolean function with a 4x1 MUX and the minterm number of 2 input external gates. Do not assume that complements are available. F(A,B,C,D) = (0,1,3,4,8,9,15)What I have done so far is drawn the truth table. At this part since there's only 4 data to be...
  32. G

    Predicate Logic: Are These Statements Logically Equivalent?

    Homework Statement Let p(n) and q(n) be predicates. For each pair of statements below, determine whether the two statements are logically equivalent. Justify your answers. a) (i) ∀n (p(n) ∧ q(n)) (ii) (∀n p(n)) ∧ (∀n q(n)) b) (i) ∃n st (p(n) ∧ q(n)) (ii) (∃n st p(n)) ∧ (∃n st q(n))...
  33. S

    Logic Function Being Implemented

    Homework Statement http://i139.photobucket.com/albums/q292/strkthug/KCL/qnumber7.jpg Homework Equations The Attempt at a Solution I can't find this any where on the web but for some reason I think it is like A*B=Y am not sure if that is correct
  34. S

    Steps for Solving Symbolic Logic Proofs

    Can someone help with this proof: G→(PVE), P→N, E→C, -(NVC) ㅏ-G This is what I have done so far 1 (1) G→(PVE) Assumption 2 (2) P→N Assumption 3 (3) E→C Assumption 4 (4) -(NVC) Assumption what do I do if here?
  35. N

    Can someone tell me exactly where my simple logic breaks down? (infinity \neq 1)

    The simple DE under our attention is DE := y(x)' = y^{1/3} \textrm{ with }y(0) = 0. Apparently this has an infinite number of solutions, but I do not understand: can someone exactly pinpoint and explain the fault in my reasoning (that follows)? Step 1: define DE2 := y(x)' = y^{1/3} \textrm{...
  36. M

    Logic design - Full subtractor question -

    Logic design - Full subtractor question - need help ! Homework Statement My professor gave my class this question but I really do not know how to solve. The circuit will perform the subtraction where A<3:0>; B<3:0>; C<3:0>; D<3:0> represent 4-digit binary number. a) Complement the...
  37. Z

    Why is 2nd First Order Logic Statement of "Infinitely Many Primes" Wrong? | Help

    Homework Statement The following are two first order logic statements of the statement "There are infinitely many prime numbers" 1. http://uploadpie.com/3PZlO 2. [PLAIN][PLAIN]http://uploadpie.com/PN5i8 Can anyone explain why the second one is wrong? Thanks for help! Homework Equations...
  38. G

    Engineering Logic circuits with Flip Flops

    Homework Statement A counter has two state outputs y1 (the more significant bit) and y2 (the less significant bit) and a control input x. When x = 0, the states of the counter’s flip-flops do not change. When x = 1, the states of the counter’s flip-flops cycle through the codes of a 2-bit Gray...
  39. L

    Treatise on Tauto Logic and the Common Beauty

    Treatise on Tauto Logic and the Common Beauty For States of the World: Let there be no honor but the will to survive. Watch those who scramble for an honor to behold when the fortune falls - leaving everything asunder as it has been in all generations. With high hopes for a scandal to...
  40. M

    Help me understand this predicate logic question

    Homework Statement I've completed the rest of this homework assignment, but I don't understand this question. Otherwise, the section consists of proofs using predicate logic. Could anyone shed some light on what this question means? The book (and the question) is available online, here
  41. J

    Question about logic and recurrence relation

    Homework Statement find a logical expression using only ∧ and ¬ operators which is logically equivalent to (p ∨ q) The Attempt at a Solution losing direction what should I first consider? There is another question about recurrent relation. Suppose that a mathematical expression can...
  42. T

    Correcting my first order logic translations

    Homework Statement Well the problem is: translate the following sentences in first order logic. I cannot verify whether they are correct or not. Maybe someone can point out my mistakes. 1. No barber shaves persons shaving themselves. (\neg \exists x)(Barber(x) \wedge (\forall...
  43. A

    Simultaneity:Confused and almost confident about my own logic

    A train is speeding to east and in the frame of train two people simultaneously look towards the top in the frame of reference of train. One is sitting at the west end and the other at the east end. In the ground frame will the events be simultaneous. My Answer: Yes Of course. My Logic...
  44. A

    Understanding the Generality of Logic Statements

    Homework Statement sorry but I'm confused is it okay if i say 2 \leq 2 or 1 \leq 2 and this example i know this is true "if p is prime then p>1" but is this true? "if p is prime then p>-20" its true right? because the generality doesn't change
  45. J

    Error in Intuitive Understanding of First-Order Logic w/ 'And' and 'If-Then

    One of the ordered field, F, property is the following (i): (i) for every x, y, and z, if both x, y, z in F and y < z, then x + y < x + z. Now please think about (i'): (i') for every x, y, and z, if x, y, z in F implies y < z, then x + y < x + z. I cannot prove that (i) and (ii) are...
  46. F

    Logic Networks/Seven Segment Displays

    Homework Statement Here's the problem: Design a logic network that can display the characters in “APPLE” on a sevensegment display unit. Write the truth table for the output functions C0-C6, minimize them by using Karnaugh Map, and implement using discrete logic gates. (Hints: Character...
  47. G

    Simplify (a+b)^c | No Squareroot Needed

    what is another way to form (a+b)^c to another simple expression? like for example a^c+b^c doesn't work because its not eqivalent to (a+b)^c (without using squareroot)
  48. E

    Logic Gates and State Tables

    Homework Statement I have been asked to create a logic diagram and state table and state diagram for two equations, with two inputs and one output. The inputs are, x and y. the output is z. Homework Equations The two equations are: D(sub a) = x'y + xA D(sub b) = xB + xA z = B x' =...
  49. R

    Did I do this CS logic problem right?

    Hi everybody, I just want to check to make sure I did this problem right. I know the answer I just need to make sure I did it formally. Homework Statement The problem goes like this: a logician is on an island with two groups of people truth-tellers and liars. He meets three individuals, A, B...
  50. S

    Designing Logic Gates for Multiple Inputs and Outputs in Homework Problems

    Homework Statement ok there are two questions. one i was able to do so which is fairly easy, since it had only two variables and one output. Design a circuit that has two inputs (x and y) and one output (f) that functions in the following way: the function f is false (0) when x and y are...
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