Logic Definition and 1000 Threads

If we have K_n denote the complete graph on n vertices, can anyone explain to me how to know how many substructures does K_n have?

Homework Statement Pidgeonhole principle: If kn+1 objects are placed in n pigeonholes, then some pigeohoe contains atleast k+1 objects. Homework Equations The Attempt at a Solution I completely understand this problem but I am not sure where or how to start. If there are n =...

Homework Statement [PLAIN]http://img408.imageshack.us/img408/5284/scan0003xp.jpg Homework Equations There are none? The Attempt at a Solution I have tried to solve this problem via making a graph, trying to outright solve the problem, i have also tried to assign variables, and...

I was discussing with my E&M professor the idea of faster than light information exchange, which of course we found to be impossible, it didn't take much analysis of the simultaneity of events as seen by Einstein to realize that faster information travel than light would completely change the...

Homework Statement In a classroom, there are nine students, A, B, C, D, E, F, G, H and I, sitting in three desk rows with three students in each row. Find their places given that - A and B are as far from each other as possible - A, C and H are at the same distance from the wall S - F is...

We know that the laws of physics are unique to our universe, that is they only hold true in our spacetime. My question is about logic and if logic holds true outside our universe unlike the laws of physics. For example, if we say that x>y and z>x then we can conclude that z>y is true by logic...

I am a physics student new to the world of electronics and I have a question that may turn out to be very simple. What I am trying to design requires that a single output given some input be held in memory for a specified time despite any differing input being sent through during that time...

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

"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...

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...

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...

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

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...

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...

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...

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...

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...

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. ■...

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...

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

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...

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.

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...

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.

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...

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...

"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...

[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...

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...

"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...

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...

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 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...

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...

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...

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...