Logic Definition and 1000 Threads

Boolean Algebra is a well known field of study in mathematical logic. In Boolean Algebra (BA), a statement can be represented by a variable; usually p, q, r, etc. Under BA each variable can have the value of either 1 or 0; i.e. the domain is the field of integers mod 2. There are many...

Observation of the growth of some beetle population suggests that discrete logistic equation would be more appropriate since these animals have distinct breeding season. discrete logistic equation: Xn+1=Xn+rXn(1-(X2/K)) the result of this equation accounts for population only season to...

From what I understand, and please correct me if I'm wrong: An "Argument" in sentential logic is a set of propositions, or premises, which logically lead to a conclusion. I took this definition from http://en.wikipedia.org/wiki/Propositional_calculus However, in my text that I am currently...

Homework Statement ##\frac{1}{2}(5)=3## , based on this logic, what is ##\frac{1}{3}(10)##? The Attempt at a Solution In real life, ##\frac{1}{2}(5)=2.5## so 2.5 --> 3 Just like that, ##\frac{1}{3}(10)=\frac{10}{3}## so 2.5 --> 3 10/3 -->x Cross multiply--- x=4 I am not very...

So this summer I plan on taking a long break from my arduino and learning some more 'ancient' and fun stuff. I plan on learning to use and make different circuits using TTL's. I have read a bit on it and learned on the basic logic gates like(using '/' as separator for the reverse) n/and,n/or...

I don't understand why I enter in an infinite loop with the following code: #include <iostream> //for cout #include <cstdlib> //for rand() #include <ctime> // for time() #include <fstream> //to write into a text file using namespace std; static const int M = 3; ofstream myfile; int...

I've started to make a "Snake" game (example: http://www.kongregate.com/games/uchiha/classic-snake-game) and reached a dead end. I'm not sure the programmatically best way of figuring out where the snake's "food" should next appear. It should of course appear anywhere on the screen that doesn't...

Homework Statement Convert f=(x'+y)(x+z)(y+z) from product of sums form, into the canonical product of sums. Homework Equations boolean logic, et al. The Attempt at a Solution This is boolean logic (so + is "or" and * is "and" etc..) There has to be some stupidly simple thing...

In school, I have been told that black appears how it is because it absorbs all frequencies of visible light and reflects no frequencies of visible light. Following that logic, if one were to shine a flashlight in a dark room where the walls, ceiling and floor were all black, one would not see...

I want to design a multiphase clock generator circuit and control logic. The circuit will have a 250 MHz clock and the circuit will generate three non-overlapping clock phrases running at 50 MHz. Each clock phase has an associated output driver that can drive up to a 10pF load with no more than...

I'm looking to write a dissertation in the field of logic (for a philosophy degree). I'm deeply interested in logic, but whenever I consider the material beyond my courses it becomes pretty daunting. I'm reasonably familiar with: *First Order Logic *Set Theory and ZFC *Cantor's Diagonal...

So I've got ((q→p) ^ (p→r))→(r→q) And I have to simplify it down as much as possible using only one logical connective for the end result (not one type, just one total). Here's been my workflow so far: ((¬q v p) ^ (¬p v r))→(¬r v q) ¬((¬q v p) ^ (¬p v r)) v (¬r v q) ¬(¬q v p) v ¬( ¬p v r)) v...

hey all, I am currently studing logic and set theory. My professor solved this question in a way that seems quit strange to me- Hope you could be of help. I attached the question in image file so signs won't be lost

Hi Folks, I am stack with following task:What is the value of x after each of these statements is encountered in a computer program if x=2 before the statement is reached? (i) if (6+2=9) then x:=x+1 . (ii) if ((3+2=5) OR (2+3=3))then x:=x+1 ...

TCR(thyristor controlled reactor) is connected in parallel with fixed capacitor to provide reactive power compensation.According to equation of firing angle in terms of susceptance is not providing valid answer in MATLAB software. please help

Hello,IS there any way to check IC [AND NOT OR gate] for errors ? Is there any method for it ?

Hi, I am designing a system to run a certain sequence when the control input is off, and then run a different sequence when the control input is on. When drawing a state diagram, for the loop where the control input is on, can the system repeat the same state twice throughout its sequence and...

Homework Statement Solve for x x(x-1)=0 Homework Equations The Attempt at a Solution x = 0 and x = 1 what I am trying to understand is the logic behind the x=0? could someone please explain that to me?

1. Homework Statement and 3. The Attempt at a Solution Simplify the equation in the following picture using karnaugh. http://i.imgur.com/1T2HKpF.jpg I divided it into two cases, one I used the square and the other I used the 2x1. Will either method work to get the solution, or is the 2x2...

Homework Statement Simplify (A+B')(B+C) The Attempt at a Solution I first expanded it and got = AB + AC + B'B + B'C = AB + AC + B'C Turns out the solution is AB + B'C (according to an online source). How do we get rid of the AC term?

Homework Statement The Attempt at a Solution Is my solution correct or can I simplify it even further?

Hi, I am introducing myself to logic circuits and I want to build a network of logic gates (CMOS) that have push buttons as inputs and LEDs as ouputs. At most there are 4 gates between a button and a LED. However, at the inputs of the 4th gate, which is a AND gate, I measure 4 V and 4 V, but...

Hello, today in class we started a topic on permutations and combinations and I have come across a way in which it could be of use to me whilst working with 'logictutor' (a premade circuit board used to teach simple logic circuits). We have an experiment tomorrow where we will investigate...

Homework Statement In each of the two following open sentences P(x) and Q(x) over a domain S are given. Determine all ##x \in S## for which P(x) → Q(x) is a true statement. ## P(x): x \in [-1, 2]; Q(x): x^{2} \leq 2; S=[-1,1] ## Homework Equations According to truth values for →: a...

Homework Statement A famous lawyer takes on an apprentice on one condition: the lawyer will train the apprentice on the business, and the apprentice will have to pay the lawyer only after she wins her first case. Right after the end of the apprenticeship, the lawyer sues his own apprentice...

Homework Statement Are these propositions, if so are they true or no? a. \sqrt{n} = 2 b. Consider an integer n: \sqrt{n} = 2 and n = 4 c. Consider an integer n: if \sqrt{n} = 2 then n = 4 Here is another question. Translate the following into a propositional expression involving...

Homework Statement I'm trying to implement the function F = A'BC+ABD+AB'D' using 3 tri-state buffers. Apparently I'm supposed to connect the buffers together and use C, D, and D' as inputs to buffers. I'm supposed to pass A and B through logic to get the input signals. I'm supposed to...

Why is it so hard to convert natural language to propositional logic. We are so comfortable in understanding and interpreting english or any other language we know. But when we need to convert it into something formal, we have to think. It does not come that naturally. Why? (I am not sure if...

Hi all, I got a BSc in Mathematical Science (not very good result: 3.00/4.00) but I'm interested to further my study in Logic and Foundation of Mathematics. Can I take MSc in Logic and Foundation of Mathematics with such result? If can, which university you guys would recommend?

When reading about Gödel's incompleteness theorem(s) a few years back, I vaguely remember reading the statement that one of their implications was that mathematics can not really be seen as "merely" logic. I think the reasoning was something like: since we have sentences "this cannot be proven...

I've to derive the following proposition in PL using the system in http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/propositional-logic-8386.html (in which Evgeny.Makarov has explained everything ever so kindly to me). I'm trying to prove $\displaystyle P \vee Q, ~(R ~ \& ~ P)...

Homework Statement Homework Equations The Attempt at a Solution I don't understand the problem. For #41, which are the premises and which are the conclusions?

I'm trying to prove $$ : (\neg P \to \neg Q) \to (Q \to P)$$ in PL. Here's my attempt: $ \left\{1\right\} ~~~~~~~~~~ 1. ~~~~~~ \neg P \to \neg Q ~~~~~~~~~~~~~~~~~~~~~~ \text{Premise}$ $ \left\{2\right\} ~~~~~~~~~~ 2. ~~~~~~ Q ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \text{Assumption for CP}$...

Hello everyone, I can't seem to understand how to do this question. Determine whether the formula F: ∃x∀y(P(x) → x = y) is true or false under each of the following interpretations over the domain D = {a, b}. (i) both P(a) and P(b) are true; (ii) both P(a) and P(b) are false; (iii) P(a) is...

Homework Statement Hello. We have been given a project in our course "Digital Logic Design", which is an introductory course to Digital Logic. We are only allowed to use gates, multiplexers, flip-flops/latches, counters, comparators, simple displays (like seven segments) etc. I am making...

1) For gravitational potential energy: ##F(r)=-\frac{\gamma M m}{r^2}##. 2) For potential energy of a conservative force-field: ##-\nabla E_p = F##. So the gradient of the potential energy is always equal to the force in that direction, just with the opposite sign. So when you move in the...

Hi here is the problem I'm working on, Let $A(x_1)$ be a well formed formula of a language $L$ in which $x_1$ is free, let $a_1$ an invidual constant of $L$, Show that the formula $A(a_1)\rightarrow(\exists x_1)A(x_1)$ is a theorem of $K_L$ on this link, the first slide as the axiom of $K_L$...

Hi everyone, I'm reading Logic for mathematician form A.G. Hamilton, at some point the book explain what a free term is, but I'm not sure how to determine if t is free or not. I was wondering if one of you may have a link where I could read more about it. (I have find some info on wikipedia...

do we assume "logic"? Mathematics has no foundations on reality, it stands on its own. But to construct it we have to assume a number of axioms, like if I wanted to create a "science" where the only rules are all circles are red and all squares are blue, then from that we can build theories and...

Alright, so I will be registering for classes at my community college here in a few days and I am having a hard time deciding on classes. I am hoping to major in mathematics or physics (leaning toward pure math) and I hope to transfer to UC Berkeley (I have a 3.7 first semester) Some of the...

Homework Statement I have to build some converters (only for 4 bits) and i didn't understand how. How do i proceed? Which logical gates combined in such a way give me the y3y2y1y0 answer for x3x2x1x0? For example, build a coverter from EXCES3 to BCD, or from GRAY TO BCD, or C1 complement to C2...

My professor wants to convert propositional statements such as X ^ Y into polynomeals such as P[(X^Y)] = xy Now, we may have multiple propositional formulas and wish to determine if they are consistent or inconsistent using Boolean polynomials. I'm having a tough time finding material...

this is not a homework question, but rather I feel like there is a contradiction in the theorem and just want clarity. I know the theorem is correct so I am looking for help in where the mistake is in my logic. take f(x) = x^3 + x^2 - 4x- 7 the rational roots theorem says if there are any...

Preparing for an upcoming midterm and this is one of the practice questions from an old test. The Question: Let X be a set with n elements, say S = {s1, s2,..., sn} Let B be the set of binary numbers with n digits. That is, sequences of n terms, each of which is 0 or 1. Define f : P(S) --> B...

Negate ## [\neg (p\wedge \neg q)]\wedge \neg r ## and relpace the resulting formula by an equivalent which does not involve ## \neg, \vee, \wedge ## attempt: ## \neg ([\neg (p\wedge \neg q)]\wedge \neg r) = \neg \neg (p \wedge \neg q) \vee \neg \neg r ## ## = (p \wedge \neg q) \vee r...

Homework Statement Number 17: http://i.minus.com/jbqSc694thPeBA.jpg Homework Equations I'm not even sure where to start. The Attempt at a Solution I know that tetrahedral shapes are non-polar if all of the attached elements are the same (e.g. CH4 or CCl4). I know all the answer...

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...

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...

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...

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...