Logic Definition and 1000 Threads

Homework Statement All married couples have fights Homework Equations let x be a person and y be another person M(x,y): x is married to y F(x,y): x have fought y The Attempt at a Solution ∀x∃y(M(x, y) → F(x, y)): i read my translation as "For all x, there is some y such that if x is married...

is this a practical way of proving math theorems? i asked because when i tried, it seemed difficult for me to decide as to how exactly i should translate theorems and given statements into logical forms and since there are so many different ways, i do not know which one is correct. For example...

Hey! :o I want to formulate the following statements into formulas of predicate logic. If a bird cannot fly, then not all birds can fly. What Donald cannot do, can no one do. John likes everyone, that is older than $22$ years old and that doesn't like those who are younger than $22$...

Hello, I am a hobby philosopher digging at the fundaments of thinking. Unfortunatly I dedected something like a new logic ("layer logic Trestone"), so I had to do a lot of formal definitions and studies. As I am rather lazy and my university time is some thirty years ago, ten years later it is...

Homework Statement A 7-segment display is used to show a decimal digit and it is driven from 4-bit input. Each bar is assumed to light up when a logical 1 is applied to it. Draw the truth table to drive segment (d) of the display.Using the truth table you have obtained, draw a Karnaugh map to...

In the paper John Corcoran & Hassan Masoud (2014): Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions, History and Philosophy of Logic, http://dx.doi.org/10.1080/01445340.2014.952947, already in the introduction it says, as self-evident, that...

Given are the following predicate symbols: Member(x) : x is a member of the bicycle club Chairman(x) : x is the chairman of the bicycle club Bicycle(x) : x is a bicycle Brand(x, y) : the brand of x is y Owns(x, y) : x is the owner of y a. Statement: every member of the bicycle club has the same...

When P -> Q, why is it true when P is false and Q is true, but why is it false when P is true and Q is false? If I suppose P mean "Jon is a guy" and Q mean "Mary is a girl". When both P and Q are true it does make sense that this proposition is true because Jon is a guy and Mary is a girl...

I'm a philosophy minor, who took first-order logic (philosophy department, not the math side) and I have a chance to take modal logic next semester (also under philosophy). It's going to be a much smaller class and will likely be harder. But it's also essential to doing work in and/or...

Homework Statement I am preparing for my final and I am stuck on the following question Homework EquationsThe Attempt at a Solution My best guess would be to make some kind of next state table, but I don't understand the relationship between xT1, yT2, yT3 and any kind of table.

Homework Statement This is from a past exam paper for logic design in my course. I have an exam coming up and would love to know how to solve this one. [/B] Develop a circuit realization of the XOR function with three inputs. You may use AND, OR and NOT-gates with not more than two inputs...

We're implementing Dots and Boxes to logic circuits and the we would like to automate the process of changing turns. If you know the game, the game changes turn when one move doesn't score a point or form two or more boxes. I was able to create overlapping XOR gates that alternates from high to...

Homework Statement I have been going through a textbook trying to solve some of of these with somewhat formal proofs. This is a former Putnam exam question. (Seemingly the easiest one I have attempted, which worries me). Consider a polynomial function ƒ with real coefficients having the...

Homework Statement Homework EquationsThe Attempt at a Solution I'm a bit confused with this. I thought a ROM was just a non-volatile storage. I don't understand how this would work. The decoder can only select one of the 8 outputs depending on what it gets at its input. I still attempted...

Homework Statement Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a "yes or a "no" response to a question a tourist asks. Suppose that you are a tourist visiting this are and come to a fork in the road. One branch leads to where you want to...

Homework Statement 1. Why is the statement: " Vicky is not clever" Not a mathematical proposition? Provide examples please 2. Why is the statement: "a^2+b^2=c^2 an indeterminate proposition?" 3. Why is the negation of " If a triangle has two equal angles it is isosceles" = "Not all triangles...

Homework Statement An explorer is captured by a group of cannibals. There are two types of cannibals--those who always tell the truth and those who always lie. The cannibals will barbecue the explore unless he can determine whether a particular cannibal always lies or always tells the truth. He...

Homework Statement We have 100 statements, where the nth statement says that "exactly n of these statements are false." What conclusions can you draw about the truth values of the statements? Homework EquationsThe Attempt at a Solution Immediately we see that the 100th statements can't be...

Homework Statement Prove that $$(\bar{a} + b)(b+c) + a\bar{b}$$ where ##a,b## can be from the set ##B\in\{0, 1\}## equals $$a+b+c$$ Homework Equations Rules of Boolean Algebra 3. The Attempt at a Solution [/B] My attempt: ##\bar{a}b + \bar{a}c + bb + bc + a\bar{b}## ##b(\bar{a} + 1+c) +...

I am studying propositional logic, and have studied how propositions can be combined with logical connectives and such, and truth tables can be used to analyze the resulted truth values, depending on the truth values of involved variables. However, when not talking in the theoretical, how do we...

Homework Statement Let ##x\in \mathbb{R} ## Prove the conditional statement that, if ## x>-1## then ## x^2 + \frac {1}{x^2+1} \geq 1## 2. The attempt at a solution Suppose ## x>-1## is true. Then ## x^2>1## Then ## \frac{1}{2}>\frac {1}{x^2+1}## Then ##x^2+ \frac{1}{2}>x^2+\frac...

Homework Statement (a) The NOR gate combination in Figure 1 acts as an AND gate. Copy and complete the truth table. (b) An aircraft door is locked by two bolts A and B each of which operates a sensor giving a logic 1 when the bolt is fully inserted. A further sensor C gives a logic 0...

Homework Statement Construct a truth table for the combination of logic gates shown above. 2. The attempt at a solution First of all the combination of logic gates with added letters to the combination: The truth table: I think it should be correct. But just want to be sure.

Homework Statement Complete the truth table for the simple combination of logic gates shown above. 2. The attempt at a solution I think this should be correct, but just want to check, since I don't have a book answer to compare:

I'm trying to solve https://www.hackerrank.com/challenges/summing-pieces and I think I have come up with an O(n) solution although the numbers aren't coming out exactly right. The problem is essentially to find a sum like ABCD ---> All sets of sets of contiguous subarrays spanning ABCD is {...

Homework Statement There is a triangle with sides $$ 3,3r,3r^2 $$ such that 'r' is a real number strictly greater than the Golden Ratio. Is this statement true or false...? Homework Equations $$Golden \space Ratio = \phi = 1.618... $$ The Attempt at a Solution Actually I have no clue at all...

Homework Statement The rules for a certain frequent-flyer club include the following statements: "Any member who fails to earn any mileage during the first twelve months after enrollment in the program may be removed from the program. Except as otherwise provided, any member who fails at any...

Homework Statement Build a circuit that either adds or multiplies two 4-bit numbers based on a control input C(C is 1 add, C is zero multiply). Numbers are positive and negative so use two's complement. You can use muxes, Full Adder Circuits, and logic gates Homework Equations Multiplier...

"For every x in domain D , Q(x) "is false if Q(x) is false for some x in D . "For every x in domain D , Q(x) "is false if Q(x) is false for all x in D . Which of the following is correct ? Or both are correct ?

Homework Statement Determine whether the following is valid: p \rightarrow \neg q , r \rightarrow q , r, \vdash \neg p Homework Equations Modus Ponens, disjunctive syllogism, double negation. The Attempt at a Solution I've boiled it down to p \rightarrow \neg q , q, \vdash \neg p...

Homework Statement Prove that ##f: \mathbb{R}\to\mathbb{R}, f(x) = x^2## is not injective. Homework Equations Definition of an injection: function ##f:A\to B## is an injection if and only if ##\forall a,b \in A, f(a) = f(b) \Rightarrow a = b##. The Attempt at a Solution ##f...

Homework Statement A straight rope is dropped at a height where is it not touching the ground. The rope has 10 beads spaced out on it and tied so they do not move. From the bottom to the top, the space between the beads increase, where the distance is the smallest at the bottom and largest at...

#define _CRT_SECURE_NO_DEPRECATE #include <stdio.h> int main() { int A; int B; printf("This is a simple boolean truth value calculator.\n\n"); printf("Please input the boolean value for statement A\n\n\n"); scanf("%d", &A); printf("Press enter to continue\n\n\n"); getchar()...

The question is about a logic game between two competing players "Abelard and Heloise", Abelard is the name given to the "For all" quantifier and "Heloise" is the name given for the "There exists" quantifier. The statement is: Is ##(\forall x)(\forall y)(\forall z)(\exists u)(\exists v)(\forall...

Homework Statement A person can either be a knight (always tells the truth) or a knave (always tells a lie). On an island with three persons (A, B and C), A tells "If I am a knight, then at least one of us is a knave". Homework Equations Truth tables, logic rules. The Attempt at a Solution...

Homework Statement We call a seven digit number in base eight X, whose digits are given by ##abcdefg## No digits are zero, and none of them are the same. The following divisibility rules are true: (I)The number ##ab## is divisible by 2 (II) The number ##abc## is divisible by 3 (III)The...

Hello everyone! I want to proof that: ##p \land (p \to q) \Rightarrow q## I know this is a quite trivial problem using truth tables, however, I want to do it without it. As I'm learning this myself, is this the correct approach? ##p \land (p \to q)## ##\iff p\land (\neg p \lor q)## ##\iff (p...

So I am studying conditionals in proposition logic, and I have discovered that there are a variety of ways to phrase a conditional "if p, then q" in English. Some of the harder ones are... p is sufficient for q a necessary condition for p is q q unless ~p (where ~ is the not operator) p only...

Hello! Some time ago I asked the admins for permission to post a link to my Logic Calculator app for android. They allowed me to post in this section so, here I am! I am a software engineering student from Buenos Aires and in my freshman year I started to develop this app as a project for a...

I know that there are several models of the real numbers, some where the Continuum Hypothesis holds, others where it does not. I would like to understand why the usual definition of the reals, limits of Cauchy sequences of rational numbers under the usual absolute value norm, isn't one of these...

Let us suppose that we are modeling a particle traversing some distance in space & that f(x)=x². Let the x-axis be time (hrs) & the y-axis be position in space (miles). What is the instantaneous velocity of said particle at t=4 hours? Let's assign variables to each coordinate in our x, y...

Hi all, Just curious on whether temporal databases are designed in the same way as "standard" relational databases, so that queries on temporal databases are wffs in temporal logic , i.e., using Until, Release and all other unary operators , and the query outputs is the set of models for the...

Question regarding different percentage changes. If I have a monthly rental fee of \$100 in July with a discount of 60%. I will pay \$40. In the month of August the monthly rental fee is \$100 with a discount of 45%. I will pay \$55. My discount has decreased by %15. However my...

Homework Statement -Admiral, your orders are to deploy the fleet into battle formation. -your fleet contains 1 battleship, 2 cruisers, 3 destroyers and 4 corvettes. -battleship requires 4 squares deployment, cruiser requires 3, destroyer requires 2, and corvette requires 1 -each ship...

I have been studying discrete mathematics for fun and I am kind of stuck on this bijection problem. 1. Homework Statement I wanted to apologize in advance if i put this homework question in the wrong part of the forums. Discrete Math and much logic math is a computer science type math of...

given a dictionary \Sigma = \left \{f(),g(),R(,),c_0,c_1,c_2 \right \} and a sentence \phi over \Sigma, I need to find an algorithm to translate \phi to \psi over \Sigma' where \Sigma' = \left \{Q(,,,), = \right \} (Q is a 4-place relation symbol), so that \psi is valid iff \phi is valid. I...

Hello Everyone, This is my first post, so please me kind :D I have an assignment and have been stuck on this thing for 2 days. I have no problems working this out with a truth table but we are not allowed to use this. So this it the expression. I understand that I have to remove the...

i need help with a proof: (pv~q)vr ~pv(q.~p) / q>r this is some propositional logic thanks all

hi! I've been studying formal proofs for my logic final and i had a question on this one that i found in my textbook: 1.)~P\supset(horseshoe)U 2.)P\supsetF 3.)F\supsetU\thereforeU i just have had a little trouble in the past getting started with proofs. Can anyone give me a little push and...

When you are proving a valid argument using the assumption reductio ad absurdem, can you assume anything in the conclusion, and then put a not in front of it, or do you have to assume the whole conclusion with a not in front of it? For example: 1. p\supset q 2. p \lor q \therefore p and q To...