Logic Definition and 1000 Threads

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.

Hi [SIZE="3"]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...

"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...

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...

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...

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...

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...

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...

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...

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...

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))...

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

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?

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{...

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...

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...

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...

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...

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

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...

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...

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

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...

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)

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' =...

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...

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...

I'm trying to negate this statement and want to make sure I'm doing it right. (p\veeq) ---> (p \wedge q) So I don't negate both sides do I or else that would just make them equal out again? So I just negated the left side, so \neg(p\veeq) is equivalent to \negp\wedge\negq So that's the...

Hello I'm reading Y. Manin's http://books.google.co.il/books?id=8NTWRFD5lZ8C&printsec=frontcover&dq=yuri+manin+introduction+to+mathematical+logic&hl=en&ei=cfp_TJ2vJ8KSjAeB-6xl&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCkQ6AEwAA#v=onepage&q&f=false" and I've been having some difficulties. So...

Homework Statement By providing a truth table, show that the following logic statement is a tautology: p ∧ (p → q) → qAny help will be much appreciated. Thank You

Homework Statement State that is either true or false The span of an empty set is empty set Homework Equations n/a The Attempt at a Solution from definition, when you span a subset of vector space, the subset must be non-empty. so, how should i answer this question? should i answer...

Hi there. I'm interested in going back to school for graduate studies and am particularly interested in Categorical Logic, that is, the application of Category Theory towards the study of Logic and Model Theory in particular (at least so far as my specific interests go). I'm also pretty...

Homework Statement I've started studying natural deduction recently and I have to prove (p implies q) or (q implies r) Homework Equations -- The Attempt at a Solution I thought about using the Law of Excluded Middle, but I'm not sure.

Homework Statement X={n/n belongs to N,X>=4} B={x belongs N/ x<5} Homework Equations then, A intersection B=________

hi I have an idea for new logic optimization algoritm, like "Quine–McCluskey algorithm" and the "Espresso heuristic logic minimizer", but it can handle multi-level representations and it can find the (theoretical) best circuit. It should work for 8 to 12 input bits. I was wondering if such...

We're all too familiar with the version of the Omnipotence paradox, the so-called paradox of the stone : Can God create a rock so heavy that even he cannot lift it? ... (1) ... which has been discussed ad nauseam in philosophy classes and on the web. Now, how about this version: Can...

Can a statement or proposition be considered a mathematical object?

or 1 = infinity Discuss

Hello, this is not homework. I am working on a personal project and had I think a fairly simple set of questions. They really are all the same, so answering one as true probably means the others are true as well, but if not please point out where and how I'm wrong. I have a very basic idea of...

I've been following the first few chapters of Yuri Manin's "A Course in Mathematical Logic for Mathematicians," and as an undergraduate who has only had basic logic and naïve set theory, the way he explained a few of the topics rubbed me the wrong way - specifically, the definitions of the...

The "logically implies" concept in first-order logic I've been reading about first-order logic (in Enderton, and in Rautenberg) and I've gotten to the point where (I think) I understand what it means for a set of formulas to "logically imply" another formula. I'm a bit confused by one thing...

I have recently read about intiuitional logic, and have a question. What is the formal form of the statement "A is non-empty", where A is a set? Could it be a pair <a,b>, where a is an element of A, and b is a proof of that a is an element of A; i.e. if A = { x | phi(x) }, then a is an...

Nearly a century ago it was found that nature obeys a particular kind of logic. Because it is related with quantum effects this logic was named quantum logic. Its axioms only slightly differ from classical logic, but this difference has enormous consequences. The structure of the quantum logical...

1. Problem Directions: Using propositional logic, prove that each argument is valid. Use the statement letters shown. If the birds are flying south and the leaves are turning, then it must be fall. Fall brings cold weather. The leaves are turning but the weather is not cold. Therefore the...

Ques) Why we cannot see our face in the newspaper and in the wall ?

Homework Statement Why is it that the output is equal to V+ (when the switch is open) in diagram A, if there is no current flowing? Why is it that A (1/0) is used by convention? I mean the lamp I got at home has a "0" for off and "1" for on, on the switch. This is confusing me...

Basically, I'm trying to generate a short pulse when the user pushes a button using a CMOS gate and a rudimentary RC charging circuit. It all simulates fine in Multisim, but I'm concerned what will happen when I run this for real (still waiting for parts in the mail). Here's the diagram...

I am hoping it may be helpful to separate Bell's logic from Bell's mathematics https://www.physicsforums.com/showthread.php?t=406372. Understanding one may better help us understand the other. Thank you Bill. In the language that is evolving at "Understanding Bell's mathematics"...

Any advice on how to make step 6 check out?

Let L = {f } be a first-order language containing a unary function symbol f , and no other non-logical symbols. 1.Write down a sentence χ of L which is satisfiable in some structure with an infinite domain but is false in every structure with a finite domain. What can you say about the size of...