Logic Definition and 1000 Threads

Here I am with another problem... :) It's from a Discrete Mathematics course and it requires a step by step proof with logical equivalences and deductions made based on the laws of logic. A,B,C and D are all on the same canoe team. They don't know what sitting order they should make and all of...

The Subject is Discrete Mathematics as part of a Computer Science major. The exercise is as follows: Erica, Stanley and Robert were all witnesses in a car crash. Their statements are contradictory to one another, and all of them claimed that someone else lied. Erica claimed that Stanley lied...

Hello, folks. I'm taking my first formal logic class and some of the things seem contradictory; I know it's because I'm not fully understanding something, but I don't know what I'm not fully understanding—I hope someone can help me. The problem begins: The statement I'm having trouble...

Let's say that a treatment A has been proven to have an impact on the levels of B with a given confidence interval. Let's also say that we know that the treatment C causes the treatment A to be imposed on our sample. Before the testing on the effects of C has been done, which statistical models...

We can use NAND gate only to get ( XOR gate ) of 2 input ( A and B ) : By using (4) NAND gate : The output of 1'st NAND : (AB)' The output of 2'nd NAND : ((AB)'.A)' = (A'B) The output of 3'rd NAND : ((AB)'.B)' = (AB') The output of the hole circuit will be: ((A'B).(AB'))' = AB'...

This is related to logic circuits. How do I simplify this boolean algebra(logic) into its simplest expression? h = (abc + abd + acd + bcd)’ My first attempt would be to change it into product-of-sum. h = (abc)'(abd)'(acd)'(bcd)' and then what next?

So I know that the Lebesgue outer measure of a set of only countably many points is 0. An example of this is the rationals as a subset of the reals.I want to make sure my intuition behind this is correct. The process: Now, if we are going to take the Lebesgue outer measure of the rationals, we...

I have a few questions regarding 2 set problems. Exercise 1: Homework Statement 1. the set A = P(empty) (the powerset of the empty set); 2. the set B = P(A); 3. the set C = P(B). 2. The attempt at a solution 1. A= {empty} 2. B = {empty, {empty}} 3. C = {empty, {empty}, {{empty}}, {empty...

Homework Statement Prove the following LEMMA: For every proposition A[P_{1}, \dots, P_{n}] and any two interpretations v and v', if v(P_{i})=v'(P_{i}) for all i=1, \dots,n, then v^{*}(A)=v'^{*}(A). Homework Equations The Attempt at a Solution Sure this is obviously an...

Homework Statement A small object, of mass 0.02Kg is at the top of a tall structure 160m high, it is dropped from rest. Ignoring air resistance.. 1. Find the speed of the object as it hits the ground 2. find the time taken Homework Equations So far we have learned the equations...

I am trying to fill in some of the gaps in wikipedia's proof of Godel's diagonal lemma, which is a crucial step in proving his first incompleteness theorem. There is a step that the wiki proof just takes for granted, perhaps because it looks obvious. But I am unable to find a formal proof of...

Homework Statement In a Hilbert System, prove: \phi[x|m] \rightarrow\forall y((y=m)\rightarrow\phi[x|y]) where \phi is a formula, y, x are variables and m is a constant. \phi[a|b] denotes the formula obtained by substituting b for a in \phi This problem crops up in my attempting to prove...

What branches of mathematical logic are there? I've taken formal logic (that is, the logic where one has various operators, like conjunction, disjunction, etc). What other fields of logic should I take to become better at mathematical logic? Which fields of logic are the most useful and essential?

There are some circuits which can be made only using sequential logic like registers and counters. But some like adders can be made both by combination logic and sequential logic. So which one is better in such cases? I guess sequential logic is advantageous but what advantage does it offer?

Hi everybody! We have a theorem in natural deduction as follows: Let H be a set of hypotheses: ==================================== H U {~phi) is inconsistent => H implies (phi). ==================================== Now the question arises: Let H={p0} for an atom p0. So H U{~p0}={p0 , ~p0}. We...

Homework Statement How to make a logic gates only using NAND gates of the following diagram. How many NAND gates I would have to use for that diagram Homework Equations The Attempt at a Solution I know that A bar bar + B bar bar =AB A bar bar B bar bar = A+B De-morgans Theorem

Hello all, I've been learning and trying to reverse-engineer the logic, nature and anatomy of a stepper motor. In my quest I am trying to figure out what any given stepper motor will draw at any given rpm with given specs about the motor. These motors come with certain specs as far as...

Hi, my name is Tim, I am new to this forum. Here's the description: I don't understand how they've done it. I realize I can plot this, but what is the logic. As a graph, I drew ln(-x) first, then added 3, so move left by 3 but that was not correct I can see they've added 3 first, move...

I was wondering where the best place to study logic at postgraduate level in the UK. As far as I know it's Manchester but I could be wrong? Thanks for any help

Homework Statement On the data sheet, name the device in Figure 9, and appropriately name the four pins A, B, C, and D according to what the device is. Check your Digital Logic book for some guidance...

Hi, I have the following math problem which I'm a hardtime finding the best way to reflect/calculate. If anyone can help I would really appreciated. Problem:I have an agreement with a supplier that he will provide a bottle per case (12 bottles in a case) and I will provide a bottle per case...

Hey, so i think this is a fairly simple question but i'd like to get it firmly understood in my head. How do you figure out the amount of combinations of digits in say a 4 digit code. with numbers 0-9... I can't think of a good way to say it, but for example you could have 0,1,2,3 or...

Homework Statement You cannot edit a protected Wikipedia entry unless you are an administrator. Express your answer in terms of e: “You can edit a protected Wikipedia entry” and a:“You are an administrator." I thought the answer would be a\rightarrow\neg e; but the actual answer is...

Homework Statement Draw a logic circuit for the case where the output, HOLD, is LOW only if the input, LOAD, is HIGH and the input, READY, is LOW. Homework Equations Truth tables for AND, OR, NAND, NOR, XOR, XNOR are known (I'm not re-typing them here). The Attempt at a Solution...

According to M-theory as I understand, the 7 additional spatial dimensions to our familiar 3 are curled up all around us but they are too small for us to see. However I have difficulty in understanding how this constitutes a "dimension" because dimensions allow additional degrees of freedom...

I was just reading an article the other day about the debate in public schools about teaching evolution as an absolute truth as it has been taght for the past umteen years. Not saying that I'm a proponent of creationism or even that I'm not, but there are some serious flaws in teaching it as the...

Hi, I've been set an assignment, part of which is to come up with a formal proof for (p \wedge q) \Rightarrow p. I have to show that the formula is either a tautology or contradiction, or contingent. If it is contingent, I have to show the smallest possible equivalent expression that uses only...

Suppose we have two points A and B, separated by ten light years. Now I shoot off a proton at .999c from A to B. From the perspective of the proton the distance between A and B is now about .3 light years. Would it get from A to B in less than four months in the time frame of the proton? If not...

Hi, Can anybody recommend me a good video lecture series on Introduction to digital logic design? I want to watch these videos before going to class.

Homework Statement Given that the variables A[2:0] form a three bit grey code to represent numerical values: i) Write down all binary combinations for A[2:0], in ascending order of numerical value ii) A three bit grey code to decimal decoder is to be designed, where the outputs X[0:7]...

Homework Statement The Attempt at a Solution If at least 3 balls must be blue, then the possible ways of selecting at least 3 blues are: r, b, b, b b, r, b, b b, b, r, b b, b, b, r b, b, b, b where r = red ball, and b = blue ball So there are 5 ways to draw 3+ blue.

Hello, I am a complete novice at formal logic and so far removed from mathematical study that I have no idea how the following should be interpreted, or read, and what its implications are: (a∨~a)∨~a⇒a∨(~a∨~a)⇒(a∨~a)⇒((a∧⊤)∨~a)⇒((a∧(b∨~b)∨~a)⇒(((a∧b)∨(a∧~b))∨~a)⇒...

Hey guys I am having todo a resit paper for a maths module i failed and I've come up against a question on my paper where I am stomped and don't know if I am down the right road or not. Its truth tables from Boolean equations. Question was: K = ( X + Y) . (X . Y) I Came up with: K X...

Homework Statement Find a counter example to show that the following is invalid: ∃xP(x) ∧ ∃x(P(x) → Q(x)) → ∃xQ(x) Homework Equations - The Attempt at a Solution Well, I have tried to find something related to properties of numbers but found nothing... Then I tried to mess...

From what I learned at school today.. Afaik NOT gate acts as an inverter, right? Which means if input is 0, output will be 1 and vice versa. My question is, if input is 0 then output will be 1. From where does the gate gets its current flow? Since input is 0. Or, it cannot be used like...

Homework Statement Prove the following theorem. If a≠0, then (a-1)-1=a Theorems proven before/axioms I am allowed to use: Existence of reciprocals axiom: there exist real numbers x and y where x≠0 such that xy=1 Possibility of division Thm: basically a-1=1/a Homework Equations I just need a...

What is the difference between the following two questions: (a) For every positive real number x, there is a positive real number y less than x with the property that for all positive real numbers z, yz ≥ z. (b) For every positive real number x, there is a positive real number y with the...

I'm sure someone has tried this, and I'm sure there's a reason it's not something that is widely used, but here's a question: Can a logical NOR gate be created by shining two lasers (an A and B input) through tiny slits (like the double-slit experiment), and determining an output at a known...

Hi, All: Just curious as to whether there is some sort of canonical extension of the standard binary connectives: and, or, if, iff, etc. , to n-valued logic. I imagine this may have to see with Lattices, maybe Heyting Algebras, and Order theory in general. Just wondering if someone...

Homework Statement Sometimes i got a question with homework if i can prove something. I got a book where the tolled me to use truthtables to see the outcome : For example : (notP V Q) <=> (P => Q) P Q | notP | notP v Q | P=>Q | (notP V Q) <=> (P => Q) 0 0 | 1 | 1...

Hi All, I'm trying to write a program that will prove that a certain mathematical formula that is entered by a student is the same as the goal formula that I want. For example, if the goal formula is: 2 * X + Y then any of this student's answer can be considered correct: -> X + X + Y...

Since I know that this will get lost in the Liar's paradox thread I wanted to separate it out from the thread: In post 18 of the liar's paradox thread Hurkyl writes:" and in post #47 he writes: I would like to know where he is going with this line of thought. A related concept I've seen...

Hi people, I'm trying to solve a logic problem but I'm having some issues with a couple of them. I appreciate if you can help me with it. 1.- (∀x) (∃y) (x=y) 2.- (∃x) P(x)→(∀y)P(y) Demostrate if valid or invalid each one. Thank you!

I am self-studying elementary analysis and am learning how to prove things. I have come up with a proof that √3 is irrational, and I believe it is valid, but I am unsure of my logic, as I have not seen it proved in just this way, and I don't have a prof to ask! So if anyone could just take a...

Hi everyone! I'm having a problem. I would really appreciate some answers. I'm thinking of changing to another major. :\ I'm majoring in Industrial Eng., which has a lot of mechanical classes at my institute. I have a very logical mind, and I like to connect everything about a subject: from...

How is uncountability characterized in second order logic?

When ever I go trying to solve a problem, especially the ones that have my mind greatly diverge into many concepts, I seem to notice myself losing contact with logic. Its like a bad dream really. I find myself attempting to solve how I am solving a problem and so on. Or at least questioning what...

[SOLVED] A hard differential equation - where is the error in my logic? Homework Statement 2xyy' + y2, where y is a function of x The Attempt at a Solution 2xyy' + y2 = 12x2 |*(1/x) => (y2)' + y2/x =12x |*ln(x), 2yy' = (y2)' => (y2ln(x))' = 12x*ln(x) => y2ln(x) = ∫12x*ln(x) =>...

Trying to study in preparation for an exam, I've been told that I need to consider the circuits a little more. So in this circuit: Would the voltage across the resistor be the voltage across V0? Or would it be the voltage across the inductor because the capacitor is keeping the resistor...

I've been trying to decide on a mathematical logic textbook to teach myself a bit. I'm taking a course on it next semester, but I have never had a logic course before (I've had some CS courses though and proof-y math courses). I'm also taking a modal logic course the semester after math logic...