Logic Definition and 1000 Threads

The truth table for implication looks like this p|q| p -> q ------------ T|T | T T|F | F F|T | T <----I'm trying to make sense of this one. My prof warned us that its strange. F|F | T I that implication means: "If p, then q" "q is necessary for p" "p is sufficient for q" "p, only...

In his book 'Concepts of MODERN PHYSICS', Chapter 1, Section 1.7, page# 22to 24, Arthur Beiser tries to derive an equation for relativistic momentum, which he finally does. But I found the situation considered by him inappropriate so is with the way he deals with it. Can anyone please tell me...

Using the formal logical structure of the original theorem, the converse, the curious inverse, and the all important contrapositive, mathematics is at a standstill. I am trying to get to this very particular coordinate without using formal logic.

Hey everyone I'm new to the forums and I came here because I completely stumped. This is basic logic but for some reason I'm having trouble with this one. Homework Statement 1) ~(A * G) 2) ~(A * E) 3) G v E / prove ~(A * F) As I go through and show each step I have to give...

hi all, I'm no logician but am interested in sorting out this problem. Say you've shown that 1. x implies y and 2. z implies w what steps/assumptions are required, in classical logic, to get from 1&2 to: 3. x&z implies y&w Do the steps require some sort of separability...

Homework Statement I am going back and reviewing some elementary material in logic/set theory. Among the problems in the quantifier section is the following english sentence to logic sentence translation: Everyone likes Mary, except Mary herself. Now, my attempt was: (∀x)[(x≠m →...

I have been thinking about this question for weeks and can't figure it out! I reckon it's decidable and in EXPTIME, but not sure how to prove this! Any help would be reallllly appreciated! (Note: the question is in the attachment) -Peter

The Logic of Believing in Free Will Please Be Aware: My “proof” here is by no means complete. In all honesty, although I have spent countless sleepless nights pondering this in my head, my thirst for knowledge and truth in the matter has only just begun. With that in mind, I kindly request...

This is a two part question my book gives as practice problem. I, however am struggling to construct logical proofs and the book does not have a key. Thanks in Advance! 2a. Construct a proof, using any method (or rules) you want, that the following argument is valid: Premises (3): –...

With the study of logic, lots of words get thrown around that I don't really understand their complete meaning. With a deductive argument the conclusion is true if the premises are true, and an argument is valid if all the inferences (and the conclusion) follow logically from the axioms. These...

Hi, I'm new to this forum. My problem led me here. Homework Statement I need to solve this, using simplifying rules. ∫ = Ʃ(0,5,6,7,13) But I always get one extra area when checking with Karnaugh map, which isn't necessary. Homework Equations ∫() = a' b' c' d' + a' b c' d +...

Consider the following scenario: There is a triplet of persons A, B and C. Person A stays on earth, while person B and C both go onto two different space missions, the directions parallel to each other. Person B travels at 0.45*c, person C at 0.9*c. The space missions are both set to take...

Hello, After reading both How to Prove It: A Structured Approach - By Daniel J Velleman, and one of the Lost Feynman Lectures on Planetary Orbits, I'm wondering if anyone could suggest to me any good books they've read (or heard about) pertaining to logic (paired with analysis), or plane...

Homework Statement Using a truth table and a karnaugh map, build a minimized circuit (using only AND and OR gates) to have an output if and only if any two inputs A,B,C,D are true (let true = 1, false = 0). Homework Equations karnaugh maps. The Attempt at a Solution My only...

I don't understand the concept (or need for) of vacuous truths/implications. Why is it that if say a statement a is false then we can conclude that any implication a => b is 'true'? Ive been reading online on this but everything has been vague so far, the most sensible explanation I've seen...

Hello all, I'm in the process of simplifying the following equation using one-point rule and other predicate logic. But I’m a bit stuck with where to start or which inference rule to use first. Please help or any pointers would be much appreciated. Thanks

Homework Statement No matter what positive real number x we choose, there exists some positive real number y such that yz2 > xz + 10 for every positive integer z. Translate the above statement to predicate logic and prove it using a direct approach. Homework Equations I don't...

Okay, so I'm struggling with understanding where I went wrong. The instructor feels like I don't understand the material and when she presented my explanation to a colleague, he too agreed with her. I would really appreciate if someone could tell me the first part of where I went wrong in my...

I want A book which gives an introduction to logic , so it answer my questions like that I have posted https://www.physicsforums.com/showthread.php?t=541777 THanks

Propositional logic urgent help please Homework Statement for every a in ℝ+: for every ε>0 : a<ε Homework Equations prove that a=0 The Attempt at a Solution is it possible to use contradiction to solve that problem, if not how can I. Urgently need help.

I would like to know the basic design structure of computer processors. My concept of a processor is that it reads some binary data from memory, performs operations on it (according to a set of instructions, which it also reads in), and then writes the result to memory somewhere. (Is this...

Homework Statement Assuming the existence of 6 digital inputs and 1 digital output, design a schematic circuit diagram using any number of 8-1 muxs (i.e. no external gates) to satisfy the following requirements:  The output is true (1) when (inputs 1 and 2 are not the same) and at least 2...

Hi! I was kind of struggling with a couple of the problems on my symbolic logic homework, and any help/hints/etc. would be very much appreciated! The same symbolizations are used as in Klenk's "Understanding Symbolic Logic" book: • = dot, meaning "and", as in p • q v = wedge, meaning...

Homework Statement Given the above circuit, implement the logic circuit with only NAND gates, and then one with only NOR gates.Homework Equations N/A The Attempt at a Solution I made a truth table but I'm pretty sure its wrong because I'm confused on how to implement the 'g' part of the...

I will try to make my OP based on the rules this sub-forum subscribes to, if not please inform me. Sorry. My question is about logic. How did we acquire it? Was it evolutionary? How is it that Japanese logicians do very much the same work as white American ones do. I am asking because logic...

http://books.google.com/books?id=Ey94E3sOMA0C&lpg=PP1&pg=PA190#v=onepage&q&f=false" Aristotle's Logic I want to know whether I have understood this right. We shouldn't be saying , "All Greeks are men,all greeks are white,therefore some men are white". So we should be saying "there are...

Simple Logic Question of Converting "or" to "and" Homework Statement As the title would have you believe it's really just a basic question. I have to write (¬q <---> r) /\ (¬p \/ ¬r) ---> (p \/ ¬q) just using "¬'s" and "/\'s" i know how to change everything else, but i cannot, for the life of...

Homework Statement Draw a logic circuit for the boolean function ((p+qr)')(pq+r) do not simplify the function first The Attempt at a Solution I got this: http://screencast.com/t/BC4akgo9J but I'm pretty sure it's wrong because of the first part how the bar goes over the whole...

Homework Statement A plane has the equation aX + bY + cZ + d = 0. A line L goes from (0,0,0) and crosses the plane at some point. L and plane are orthogonal. express the coordinates of the crossing point P by: a, b, c and d. Homework Equations |d|/sqrt(a^2 + b^2 + c^2) is the distance between...

Hello, I would like to know about a good introductory book on mathematical logic. It should start from set theory , include ZFC axioms and also touch on Godel's theorems.

Tell if this Argument is valid (Propositional Logic)? P = If a man is bachelor he is unhappy Q= if a man is unhappy he dies young C = so the conclusion will be Bachelors die young is his right ? This we have to write this in this form is this correct ----> means implies Q ---> Q Q...

I am searching for physical realizations of universal logic operations (phase rotation, CNOT, Hadamard) in single-dot excitionic qubits. Phase rotations are easy to implement with sinusoidal electric fields but my literature search for CNOT and Hadamard gates runs dry. I can find them in spin...

The professor for my symbolic logic course requires us to be extremely precise with our explanations. Given the subject, I understand his reasoning and appreciate his rigor. I am studying for our first exam by doing some of the exercises at the end of the sections on which we're going to be...

Hi, All: I am trying to understand better the similarity between the compactness theorem in logic--every first-order sentence is satisfiable (has a model) iff every finite subset of sentences is satisfiable, and the property of compactness : a topological space X is said...

I have a problem that states: Write each english sentence in symbolic form using the following predicates: m = Melissa p = Pizza S(x) = ' x is a student ' L(x, y) = ' x likes y ' E(x, y) = ' x eats y ' Take A as the universal quantifier in this problem and M as the existential...

I have some difficulties to understand the logic of the solution to this problem. Q:The graph of a(x2 +y2)+bx+cy +d = 0 is a circle if a 6= 0. Show that there is a circle through any three points in the plane that are not all on a line. solution:Insisting that the graph of...

It's possible that I'm not understanding the diagram and their reasoning, but I wanted to check with some people here before I come to a conclusion. Homework Statement Homework Equations The Attempt at a Solution I don't understand why the book says the formula is false, yet there is a "T"...

If you take a look at the attachment that I have posted, you will see 4 wave diagrams labeled A, B, C, D, respectively. My objective to is to answer the questions after the A-D diagrams. The first one is a AND logic gate with A and B. So how would I combine A and B. Do I draw only the highs of...

Hello everyone! This is a pretty strange question, perhaps. I've studied logic and know very well the difference between A --> B and B --> A. However, there's a specific problem that I often encounter in proofs in maths that I find strange. For example: you get a certain P.D.E. and want to...

1. Homework Statement . 1. Let a and b be constant integers with a \not = 0, and let the mapping f : Z \rightarrow Z be defined by F(x) = ax + b. Determine all values of a such that f is a bijection. Prove that the aforementioned values are the only possible values resulting in a bijection. The...

Homework Statement All integers beginning with 1 are written down in succession. What digit is in the 1955th place? Homework Equations The Attempt at a SolutionI'm pretty sure it is 4 Wondered if someone wants to double check

Hi there I'm currently doing a digital fundamentals paper and I was wondering if anyone could identify a logic symbol on the spec sheet attached, and what's it used for. It's on page 4, and the logic symbol is a diamond that is surrounded by 4 traingles. Theres eight of them and it's near...

(x∈R → f(x)>0) → f is asmani. What does it mean: 1. If there exists some x in R such that f(x)>0, then f is asmani. 2. If for all x in R we have f(x)>0, then f is asmani. 3. It's ambiguous or meaningless. 4. ...? Thanks in advance.

Homework Statement Produce the given truth table (given below as well as in a neater version in the attached Excel document) using the Boolean operators AND, OR, and/or NOT: A (Input 1) B (Input 2) O (Output) 1 1 0 1 0 0 0 1 1 0...

What are some ways you intertwine logic into syntax, so the two can work together? Does pseudo code help?

Hi there. I need help deducing an argument form in formal language, but I am not sure that I can communicate the example very well, nor even that it can be expressed in a formal language for that matter. The case at hand: Rene is a cat. Julie is not a cat. Therefore, julie is a...

I recently read a research summary about using magnetic fields to briefly maintain quantum states in relation to quantum computing. The article makes reference to "a" simultaneously being "a" and "not 'a'". I'm left wondering how the concept of superposition is reconciled with conventional...

I've always been a creative person since I was little. I really wasn't noticed for my potential for maths at all when I was growing up and it was a year before I completed my GCSE's I was stuck in set 2 maths with a predicted grade of a D but tried and got a B all in all. When I went into...

So I got a ticket a few days ago for running a red light, the yellow light was very short, I'm trying to figure out if the city set the yellow light too short to be reasonable. The speed limit at that location is 50 mph, the yellow light is 4 seconds. Federal motor vehical safety standards...

Homework Statement You always see slope represented as \frac{\delta y}{\delta x}. Is there any particular reason for why the change in "y" is in the numerator and the change in "x" in the denominator? Why couldn't we represent it as delta x over delta y? Homework Equations \frac{\delta...