Logic Definition and 1000 Threads

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

One of the ordered field, F, property is the following (i): (i) for every x, y, and z, if both x, y, z in F and y < z, then x + y < x + z. Now please think about (i'): (i') for every x, y, and z, if x, y, z in F implies y < z, then x + y < x + z. I cannot prove that (i) and (ii) are...

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...

1. Homework Statement Let L = {P } be a first-order language with a binary relation symbol P as only non-logical symbol. By exhibiting three suitable L-structures prove (informally) that no two of the following sentences logically implies the other (i) ∀x∀y∀z(P (x, y) → (P (y, z) → P (x...

So I've been discussing this alleged proof with another person, and I was wondering what are the issues with Dr. William S. Hatcher's proposal. His entire process can be found http://www.onecountry.org/e102/e10214xs.htm", but it can be summed up into three axioms 1) Principle of sufficient...

Homework Statement http://www.play-hookey.com/digital/electronics/dl_gates.html revered members, in the above link, for OR GATE, when either of the diodes are forward biased we get the output voltage as logic HIGH. but for AND GATE, when when either of the diodes are forward biased or...

fuzzy logic can be emulated with "standard logic" if fuzzy logic can be emulated with "standard logic" then how can it be fundamentally different? shouldnt any newly proposed logic system, by definition, be impossible to model with another logic system? If you can emulate it then its not...

The following is from regulations regarding setting up a Roth IRA "Withdrawal of earnings prior to five years and age 59½ are subject to penalty and income tax." I read that to mean: Withdrawal of earnings (prior to five years) AND (prior to age 59½) are subject to penalty and income tax...

Assume ideal gas and isothermal : \Delta H = \int_{T_{i}}^{T_{f}}\! C_{p} dT = 0 (no change in temperature, no change in enthalpy) \Delta H = \Delta U + W, U = 0 There is no change in internal energy but there is change in work done. How do these two contradicting statements work.

I have ~(P&Q) and I want to get ~P v ~Q (& means and) (v means or) Am I right in thinking that I can: 1.~(P&Q) Main assumption Sub derivation 2..Assume P&Q 3.Reiterate ~(P&Q) End sub derivation 4.Then do 1-2, ~I (negation elimination) to get ~P 5.then do vI (disjunction...

Hi all, I was puzzled by the answers offered by an assessment book on this 2 questions. Hope fellow forummers can help me out on this please. 1. A thin steel card is made to vibrate by holding it against the teeth of a cog wheel. The wheel is rotated with increasing speed. The sound wave...

Homework Statement Assume you have a symmetrical clock at 100MHz. Design a logic circuit with four outputs of clocks at 100MHz, 50MHz, 25MHz, and 12.5MHz. The logic circuit should have 2 inputs to select output clock rate. Homework Equations N/A The Attempt at a Solution For...

Homework Statement Using NAND, AND OR, &/or NOR gates build a vote counting machine. It should light an LED when majority votes are true (or answer "yes"). Assume 4 input votes only. Homework Equations Boolean Logic The Attempt at a Solution So I know the solution in terms of...

Do a derivation showing that (P conditional Q) v P is a theorem of system SD+ *Sorry guys, I can't figure out how to do the symbol in between (P Q), but it means If P then Q and it is otherwise known as the conditional -I am really struggling with this problem and I would greatly...

I am confusing the heck out of myself here. This is what I have Square matrix that is M = 'm x m' A column vector that is C = 'm x 1' a smaller square matrix that is R ='r x r'Here is what I am trying to accomplish; I usually do this by hand: The entries of the column vector C are either 1...

Homework Statement Ive been asked to create a roaming 7 day alarm for college. This alarm must trigger a lamp (output), after the input, which i am using to simulate an alarm, has been pressed 10 consecutive times in a 7 day period. if it is pressed less than 10 timesin a week, then any...

Hi PF. This is a homework question, but it's for symbolic logic. Figured that it didn't really make sense to post it with the math and science questions, although I'm sure people on there would know how to solve it. I'm having trouble constructing a derivation for the following: For all x...

Every few years I Google this book and then ask about it book here on PF on the off-chance that someone recognizes it. I cannot nail down anything specific that Google can work with, so ultimately it fails. I'm going to try something different this time that should improve my Google search...

Hi there, I'm having some issues with logic functions in matlab. I don't use them very much so I'm not too familiar. What I'm trying to do is create an 'm' file for a physics project and I would like a certain progression. I'm trying to create some 'if' statements to do this. So first of all I...

pretty new to this whole computer architure thing, so i appreciate the answers given to my previous question, went through a lecture today in class, came out pretty clueless...what i would like to know is how exactly would the block diagram for a four bit adder circuit look? thank you for...

Clarification: Not a religious god, but the first force. Starting question: What was the original cause that started everything, how can there be an original cause without god? Case A: There was no original cause; the universe always was and always will be. Result: No god. Case B...

What do "two-level" and "multi-level" gate circuits mean? I have been doing questions relating to logic gates circuits, and have noticed that some questions say "implement with two-level NAND gate circuts" And then a different question would say "implement with multi-level NOR gate...

When it is fitted to supernova observations, our standard picture of the cosmos tells us that the current boundary of the universe which can affect us is at z = 1.73. As of today, no event that occurs beyond that limit can ever be known to us or have any causal effect. This is primarily based...