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.

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  1. 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...
  2. 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...
  3. R

    Engineering Diode logic doubt (digital circuit)

    Hello guys, I'm not getting the output of the diode logic circuits: http://upload.wikimedia.org/wikipedia/commons/1/1f/Diode-OR2.png If both inputs are 1, then there is current across the diodes then the output is 1, but shouldn't it drop because of the resistor R? If both inputs are...
  4. 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...
  5. B

    Designing a CPU Using Multimedia Logic - Need Advice

    I have recently been commanded with the task of designing a simple single cycle CPU to implement a sorting algorithm. We must design the project using multimedia logic. I have an idea how to design the processor, but I have no idea how to use this software. From my basic understanding of it, it...
  6. C

    Need help in simplifying circuits with logic gates

    hi, I am new in basic electronics course. i m having some problem with simplifying the circuits using boolean algebra. can you suggest me any good book to practice this? and i also need a short chart of the laws.
  7. S

    MHB Prove the following Logic Property

    Prove the following logic property using a Truth Table (perfect induction). What is this property called? x + y * z = (x + y)(x + z) My Answer: Distributive Property? Truth table. x y z f [0]0 0 0 0 [1]0 0 1 0 [2]0 1 0 0 [3]0 1 1 1 [4]1 0 0 0 [5]1 0 1 1 [6]1 1 0 0 [7]1 1 1 1 By truth...
  8. M

    Where's the logic in this Boundary value problem?

    Considering the classic problem in Electrodynamics "Conducting sphere with Hemispheres at different potentials" How does one think in order to attack this problem? I didn't get it. What potential was considered in solving this problem? Was it the +V or the -V? Or both? Why is θ' considered...
  9. K

    Logic Gate Sim: Get Boolean Algebraic Expression

    any logic gate simulator that gives you the boolean algebraic expression at the end?
  10. QuarkCharmer

    7 segment display + logic gates

    Homework Statement I'm tasked with creating a logic network that can spell out a simple 4 letter word. It has 2 inputs A and B, and 7 outputs (for a 7 segment display). The 2 bits (A and B) give the 4 total possible inputs to the circuit. Write the truth table for the 7 output functions...
  11. J

    (Symbolic Logic) Proving P v P = P (Idempotency) using a direct proof

    Ok, so it's very easy to show P v P = P (where = is logically equivalent) using a truth table as well as using a conditional proof. P v P Premise ~p Assumption p Disjunctive Syllogism (1, 2) p & ~p Conjunction (3, 4) ~p --> (p & ~p) Conditional Proof (2--4)...
  12. M

    Disc Math Logic statements (Homework check)

    My solution d. \forallx\existsy(F(x)^S(y) → \negA(y,x)) e. \existsx\forally(F(x)^S(y) → \negA(y,x)) f.\existsx\forally(S(x)^F(y) → A(x,y))
  13. M

    Is My Statement Equivalent to the One in the Paint Document?

    Can someone tell me if my statement is equivalent to the one in the paint document? My statement: x and y will define all people P(x): "x is a parent" F(x): "x is female" M(x,y): " x is the mother of y" My answer is boxed in the paint doc (SECOND POST)
  14. S

    MHB How Does De Morgan's Law Apply to Probability Logic?

    If τ(¬p)=1-τ(p) and τ(p∧q)=τ(p)∙τ(q) show that: τ(p∨q)=τ(p)+τ(q)-τ(p)∙τ(q)
  15. M

    I hope this helps!Translating Statements into Logical Formulas

    Is the statement "if you are a comedian then you are funny." equivalent to what is defined in part (a)?
  16. C

    Convert sentences into First Order Logic

    Hello there, I have 3 sentences. They are: 1) If someone is not in the class then that person is either ill or lazy. 2) Ill people do not go for shopping. 3) The class teacher noticed that James is not in the class but she has seen James come out of the Candy...
  17. alane1994

    MHB Solve Fun Logic Puzzle: 111 People & 4 Jewels

    There are 111 people in a competition. The competition has 4 boxes and 4 jewels. Each box is identical and is completely opaque (i.e. you cannot see inside the box once it is closed). The jewels are all different: diamond, ruby, emerald and topaz. Everyone in the competition knows this. The host...
  18. M

    Discreet Math: Logic Terms Memory Tips

    For anyone who has taken discreet math are there any easy ways of remembering all the terms for the condition statement? I added the terms in the paint doc.
  19. J

    When Does Set-Theoretic Logic Hold for Infinite Sets?

    Hi, Consider the following two logics: Logic 1: Given an infinite countable set of real number A = {a1, a2, a3 ... } If there exist a real number M such that: a1 + a2 + a3 + ... + an < M for all integer n, then the infinite sum a1 + a2 + a3 ... < M Logic 2: Given an infinite collection of...
  20. S

    Integration described by first-order logic?

    Is it possible, to describe a Riemann integral with just first-order logic? And if so could someone point me to somewhere that has such a description of it.
  21. C

    Looking for the logic behind this

    We got a bunch of balls numbered 1 to n. And we got a bunch of bowls numbered also 1 to n. What is the chance of ball x hitting bowl x after dropping each ball randomly in a bowl one by one? The answer involves saying 1/n after going (n-1)!/n! and I wonder, what is the full logic behind it...
  22. H

    Role of classical logic in studying logic

    Greetings, Two or three years ago I studied mathematical logic using Kleene’s “Mathematical Logic”. I was thinking about the subject again recently, and I have a question regarding what research has been done into non-classical logic. I am having difficulty phrasing my question, so please let...
  23. A

    Inter Logic Block Synchronization

    Hello, I'm trying to design a simple digital circuit for learning purpose, and maybe later a bigger project. The idea is to interface a microprocessor, probably a pure combinational logic block to do simple stuff, with a memory chip. Now what I need is a way to make sure that when I send an...
  24. G

    Logic Resolution rule application

    Homework Statement Hi, there there is one question, which I find it to be solvable, but the answer is that it cannot be solved. Can someone explain me the answer given. I think there is a mistake on the underlined row, which leads to wrong answer. I am not sure, so if someone can help me I...
  25. Tesladude

    Compact Logic Gate Options for Efficient Circuit Design

    Hi I am learning about logic gates and am having some fun with them but somtimes in my designs I only have use for maybe 1 or 2 gates, this is not convenient sense the chips I use have 4 or 6 gates in one chip, does anyone know where I can find NAND, AND, and inverter gates in 8pin dip or less...
  26. C

    Can someone explain the cognitive logic of the math here?

    Can someone explain the "cognitive" logic of the math here? I find it impossible to concentrate or learn math without understanding the underlying meaning as much 'physically' as possible (I wonder if that's a problem or a virtue by the way). I had to prove that 1/P(A) + 1/(P(A') >= 4 given...
  27. R

    Chandrasekhar's Transitivity Logic

    I've just started reading Chandrasekhar's Introduction to the Study of Stellar Structure, and I'm having trouble following one of his mathematical assertions. Rather than quote the relevant parts in their entirety here, I've typeset them and linked them...
  28. Mathelogician

    MHB Question on substitution of variables in natural deduction of predicate logic.

    Hi all, I need Explanation on the attached image from Van Dalen's Logic and Structure; specially on how the red part follows from the lines before it! Regards.
  29. B

    Proof Logic: Proving w/o Truth Table?

    Please take a look at this proof: The thing I do not get is how they can do it so fast. If I were to prove this using a truth table, I would have to use 16 rows, becuase of all the possibilities, however they seem to not have to take into account a lot of the possibilities when they prove...
  30. A

    120-240VAC Digital Logic Power Relay Timer

    Design Goal: Remove power from 4 washing machines and 4 dryers using relays and a digital logic timer. (9 Hour cycle of no-power from 22:00 to 07:00 the next day) Design Problem: What relays can I use that can be actuated by logic voltages? Should I use 2 relays, a logic relay that actuates a...
  31. B

    Can a Dog Conclude It's a Cat Using Logic?

    Homework Statement This question may sound weird, but please bear with me. Let's say that you are a dog, and you think to yourself. "All cats have four legs, I have four legs, therefore I am a cat." Obciously this is wrong because even though all cats have four legs, there are more...
  32. Mathelogician

    MHB Universal Quantifier Intro: Natural Deduction in Predicate Logic

    In Natural deduction in Predicate logic we have a rule which says [assume the set of hypotheses to be H) if H implies phi(x) then H implies [for all x phi(x)] such that x doesn't belong to FV(psi) for all psi in H [indeed such that x occurs free in no one of formulas in H] In other words, if...
  33. Mathelogician

    MHB A question on "Change of bound variables" Theorem (predicate logic)

    Hi all; I need some clarification in red part; in how it is deduced from the theorem 2.5.6! I know how the blue is deduced from the theorem but don't even know how to get blue form red in practice!(No algorithm is suggested...) Anyway, any explanation is thanked... Regards.
  34. Mathelogician

    MHB A question on substitution in predicate logic

    Hi everybody! I am confused about what is the role of the condition " xdoesn't belong to FV(phi)" in theorems like (i),(ii) or similarly in (iii) and (iv) . I know that the philosophy of the condition "the variable z's being free for x in phi" is to avoid the phenomenon that a free variable turn...
  35. S

    What is Symbolic Logic Useful For?

    My (soon to be) university offers a class called, "Symbolic Logic," that fulfills the GER quantitative reasoning portion of our school's requirements. I'll be an incoming freshmen next academic year and was just an average math student in high school. Honestly, I just didn't put in that many...
  36. J

    How to Toggle PLC Outputs with a Single Button Using an Internal Bit?

    I'm 4 days into an Introduction to PLC's class and have been doing well, but have now been stumped. I've attached a .jpg to show where i am on this problem. Use only XIC,XIO,OTE and branching circuits Pressing N.O. PB00 once should latch on output LT08; pressing PB00 a second time should...
  37. N

    Mathematics to be simply an extension of logic

    Hello, I read that many people believe mathematics to be simply an extension of logic and therefore some or all of math to be reducible to logic. I thought this was an obvious fact for the longest time. I was wondering if there was any flaw with such an argument or what else there is which...
  38. B

    Engineering Full adder circuit using NAND v NOT, AND, OR v PLA logic

    I have designed a full adder circuit, first of all implementing NOT, AND, OR logic, then redesigned NAND logic and finally Programmable Logic Array. I would like to talk evaluate my designs a little and need a bit of help. When using NOT, AND, OR gates I used the following; NOT x 3 = 1...
  39. R

    Mathematical Logic and Structures

    URGENT ! Mathematical Logic and Structures Hey guys, i need a HUGE favor, i need the resolution for this 5 questions, its a question of end this year my degree or stay one year just with a subject. Please I am begging, who knows the resolution please say me something. Part 1...
  40. R

    Mathematical Logic and Structures

    URGENT ! Mathematical Logic and Structures Hey guys, i need a HUGE favor, i need the resolution for this 5 questions, its a question of end this year my degree or stay one year just with a subject. Please I am begging, who knows the resolution please say me something. Part 1...
  41. U

    Derive all four propositional logic operators from nand

    So I recently learned that you can derive all four of the propositional logic operators (~, V, &, →) from Nand alone. As I have understood it, so long as you have negation, and one of the other operators, you can derive the rest. Like P → Q can be defined as ~P V Q. However, I learned that...
  42. A

    Solving DRL Logic Problem: Get Help Here!

    Hi Guys, I'm solving a DRL related problem https://dl.dropboxusercontent.com/u/49829206/skitch.jpg I though the output diode were in forward . but I suddenly noticed that it's in reverse .. so I couldn't handle the answer. can anybody help,please?
  43. F

    MHB Logic involving knowing when a form is ready to be submitted

    I am creating a form using IBM Form Experience Builder. I want to create a survey as follows (content in [] denotes possible answers) Do you still require a specified asset? [yes/no/I'm not the owner] Do you know who the owner is? [yes/no] Specify: [] Survey is complete The...
  44. F

    Exploring the Origin of Numbers: Logic and Set Theory

    Where do numbers come from? What is the logical basis for the existence of numbers? Are numbers defined in mathematical logic as the cardinality of set? For example, it would seem to me that 3 is defined as the cardinality of any set that has 3 elements. IIRC it was Whitehead and Russel...
  45. nomadreid

    Modal logic K4: strong box quantifier

    In an exposition about the modal logic system K4, after introducing the box "necessity" quantifier \Box (where \BoxP is essentially that the Gödel number of P is provable), then introduces the "strong box" quantifier [s] (I don't know how to put an s inside a box in LaTex) as: [s] A = A \wedge...
  46. M

    Real-world logic problem with statistics and groups

    First let me apologise for the improper use of 'groups'. I'm not a mathematician but I know that 'groups' means something specific. Anyway, here is my problem. The exact circumstances of my problem are esoteric and bothersome to explain, and I don't want to distract you with details that do...
  47. B

    Tri-state logic: High impedance as an input to a logic gate

    So I am well familiar with how bi-state logic (with 0s and 1s) works in gates. 0+0=0; 0+1=1+0=1+1=1 etc. What happens if an input to a gate is neither 0 nor 1, but has an high-impedance value? Will it disable the logic gate from working? Will the logic gate simply ignore that input? Anyone...
  48. I

    Is This Boolean Expression Simplified Correctly?

    The boolean expression I am working with is: ((ab)'(b'c)' + a'bpc') where ' is the NOT symbol. I have the following logic circuit diagram. Is it correct?
  49. V

    Interesting logic puzzles and brain teasers

    I thought it would be cool to start a thread with a bunch of interesting logic puzzles, brain teasers, math problems, etc. I'll get the ball rolling: Solution: http://www.mindcipher.com/puzzles/141
  50. F

    Medical I am obsessed with logic and it makes me violent

    Whenever I argue with people and they resort to logical fallacies, I get extremely frustrated and even violent. I have no problem accepting different opinions as long as they are defended in a logical way. What ticks me off specifically is logical errors, fallacies. I can't stand when logic...
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