Logic Definition and 1000 Threads

I want to do tricky physics and maths questions that require only A-level knowledge of maths and physics to solve. Questions that don't have a straightforward answer and will help me to develop my logic and problem-solving skills. I'm looking books, online resources and etc.

Homework Statement Homework Equations The Attempt at a Solution E4Πr2 = Q/∈0 49000⋅4Π4.12 =Q/∈0 Q = 91.6 μC Qshell = Q = 91.6 μC Qshell = Qinner + Qouter 91.6 = -3.3 + Qouter Qouter = 94.9 μC Can someone point out the error? I have skipped too many lectures and I am catching up right...

Homework Statement You’ve decided to protect your house by placing a 5.0 m tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you’ve learned that lightning bolts can carry up to 50 kA of current and...

Hello everyone. This is my first post on this forum. Thank you for taking the time to help me with my question. I have no idea where to start. :( Question 1: Find an example of a predicate P(x,y) where the domain of x and y are D such that $\forall x \in D, \exists y \in D, P(x,y)$ is true but...

So once again this is my homework: If you could please check these answers and help me with Q.9 part 1 Q.8 is just checking if both expressions give the same values right ? Q.9 part 1 I'm in the blind here Q.9 part 2 seems logical Q.10 So if i get this right... for the statement/argument to...

So , what I was wondering about was a slight difference in notation, for which I am not certain if correct (mine, in particular.). The induction axiom says: If M is a subset of ℕ, and if holds that: a)1∈M b)(∨n∈ℕ)(n∈M→s(n)∈M) then M=ℕ. Now my question is: why do we write (∨n∈ℕ)(n∈M→s(n)∈M)...

Homework Statement My solution, is this correct? This is what I came up with. Y=A+((A*B)+B+C'+(B+C'*D)+D) Is it safe to say that it is correct or did I make a mistake?

Homework Statement Rewrite the following statements in symbolic form: a) If ##a## and ##b## are real numbers with ##a \ne 0##, then ##ax+b=0## has a solution. b) If ##a## and ##b## are real numbers with ##a \ne 0##, then ##ax+b=0## has a unique solution. Homework EquationsThe Attempt at a...

Homework Statement [/B] "Use the truth table method in Boole to determine whether the conclusion is a tautological consequence of the premises." (Tet(a) ^ Small(a)) v Small(b) ------ Small(a) v Small(b) Homework Equations [/B] Taller(claire,max) v Taller(max,claire) Taller(claire,max)...

Hello, Student looking for help and absorbing as much information as I can to get me through a Symbolic Logic course that is currently kicking me butt. Using tools such as Tarski's World, Boole and Fitch. Anyone with experience feel free to contact me. Thanks

It is assumed that entropy increases in the universe. However, the fluid and acceleration equations are derived assuming that. TdS=dE+pdV where dQ = TdS. But dQ is usually set equal to zero to derive these equations. Hence since T is non zero, dS should be zero and so there would be no...

So, here's my question. I read somewhere that all universal truths on empty domains are vacuously true, whereas all existential are false. However, if all statements of the form (∀x∈A)(P(x)) , where A is an empty set, are vacuously true, then the statement (∃x∈A)(P(x)) should also be true...

Homework Statement I have to prove that ##(p \equiv q) \equiv ((p ∧ q) ∨ (¬p ∧ ¬q))## With no premisses In order to prove this, I first need to prove that: ##(p \equiv q) \to ((p ∧ q) ∨ (¬p ∧ ¬q))## And: ##((p ∧ q) ∨ (¬p ∧ ¬q)) \to (p \equiv q)## I was able to find the second implication...

Homework Statement A 1000 kg car approaches an intersection traveling north at 20.0 m/s . A 1200 kg approaches this same intersection traveling east at 22.0 m/s. The two car collides and lock together. Ignoring any external forces , what is the velocity of the car immediately after the...

Hi, why a wired-logic gate does not produce a physical second-level gate ? Is it due to the velocity of the components that create the "wired-connection" ? Thanks

The sentence is : "For all real numbers there exists a natural number that is smaller". That is (∀x∈R)(∃n∈N)n>x. This is what I thought of: we can write this sentence as:"If x is a real number, then there exists a natural number n that satisfies n>x." So how would I make a converse statement...

Homework Statement A thin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. The rod (A) has a thermal conductivity of kA = 0.15 W/(m*K), while the tube (B) has a thermal conductivity of kB = 1.5 W/(m*K) and its outer...

Hello guys, I really need help from you about natural deduction. I just can't get to solve theses problems. Can anyone give me the solutions ? I've been trying for hours... Thanks a lot ! Premise 1 : B, Premise 2 : C→(¬B∨A) Premise 3: ¬C→¬(A∨B) Conclusion : A≡C ____ Premise 1: (A∨B)∨C...

What mathematical logic texts do MHB members think are the best at undergraduate level ... that is the best introductory texts ... Peter

Homework Statement Hi all, I came across these steps in my notes, relating to a step whereby, $$\hat{G} (k, t - t') = \int_{-\infty}^{\infty} e^{-ik(x - x')}G(x-x' , t-t')dx$$ and performing the following operation on ##\hat{G}## gives the following expression, $$[\frac{\partial}{\partial t}...

https://en.wikipedia.org/wiki/Fitch's_paradox_of_knowability It begins by assuming that 'All truths are knowable' and then logically proves that that assumption means 'All truths are already known.' The proof is like this: Suppose p is a sentence that is an unknown truth; that is, the sentence...

Hello! I'm just starting out on this logic train and I'm not sure I'm grasping it correctly. I took a statement and attempted to convert it into the symbols below. ∀x∈ℤ,∃y∈ℤ,(E(x)∧E(y)) → x = 2y The original phrase is: Any even integer is equal to twice some other event integer. Which I...

Dear Everyone, I need to translate this following statement into a symbolic logical form of the statement: The square of every odd integer is one more than an integral multiple of 4. Thanks, Cbarker1

Let me start by saying that this is from a 30 question assessment on Big Oh, Big Theta, and Big Omega. I understood every other question, however, even after being given the correct answer, I do not understand why my answer was wrong for this one. If you could point me in the direction of any...

Homework Statement Ok so I remember learning KCL. Current is either entering or leaving the node. There's only two possible option. You can call entering the node positive or negative, you can call current exiting the node either positive or negative. As long as what you call entering the node...

Good day. I'm currently in the soldering phase of an RF circuit designed to operate an L293D motor chip. On the breadboard I managed to get it to work, but after soldering (and checking for shorts) I am not getting proper high/low signals sent through the encoder/decoder from 2 2p2t switches to...

I'm reading Velleman's book titled "How to Prove it" and I'm very confused when I'm reading about conditional statements. I understand that there exists some issue with the conditional connective and I accept that because that's the cost of espousing a truth-functional view. I came here to ask...

1. Suppose P(x) and Q(x) are propositional functions and D is their domain. Let A = {x ∈ D: P(x) is true}, B = {x ∈ D: Q(x) is true} (a) Give an example for a domain D and functions P(x) and Q(x) such that A∩B = {} (b) Give an example for a domain D and functions P(x) and Q(x) such that A ⊆ B...

Homework Statement [/B] I am currently working on an assignment in which I create a six-state up/down counter. The purpose is to understand the functionality of flip-flops within a circuit among other things. There are 3 input bits (Q2,Q1, Q0), and a 4th control bit (C) which determines the...

Homework Statement Pat beat Stacy in a set of tennis, winning six games to Stacy’s three. Five games were won by the player who did not serve. Who served first? source: https://ocw.mit.edu/courses/mathematics/18-s34-problem-solving-seminar-fall-2007/assignments/hw8.pdf Homework Equations N/A...

Hello, all. I am looking for some good books to start becoming invested in mathematical logic, the foundations of the field of mathematics, and also basically in general the philosophical heart of this wide subject which has interested me greatly. Now I have already read Shoenfield and Halmos...

I was working on https://www.hackerrank.com/contests/101hack50/challenges/even-and-odd-boxes for 2.5 hours and couldn't get it right. The programming competition is over, so now it's ok to discuss. I can't figure out where I was going wrong. static void OnesToFront(List<int> list) {...

I am trying to implement the following circuit in Logisim, yet all I get is y=0. Any idea what might be the problem? First image is what I am trying to implement; second it my Logisim attempt which yields 0. I'd appreciate some feedback.

Hi All, When a query is made in SQL , it is transcribed into FOL in the back end , and, if the transcription is a wff , the models, if any, are returned as the answer to the query. I have an idea of how the transcription works for basic statements, but, does anyone know the actual "...

I have a small problem with the first order logic, in particular, predicate logic Let us take this sentence as an example: Each teacher has given a form to each student. From this sentence, can we have different reading? This is my try to solve such problem, I did not know if this is the...

Andrei has a bag of x sweets. He removes two sweets from the bag simultaneously (without replacement). He now removes a third sweet. The probability that the third sweet is red is (x/2) - 1. How many red sweets were in Andrei's bag to begin with? Could somebody please tell me if (and how) it is...

Lately, I've been hooked on Douglas R. Hofstadter's book Gödel, Escher, Bach. In it, he discusses the idea of "strange loops"—often apparent logical paradoxes—and argues that they are the key to understanding consciousness. He includes witty dialogues, as well as examples of "strange loops" in...

Homework Statement The block diagram of FIGURE 3 shows a three-stage asynchrononous counter that is used to count a series of randomly occurring input pulses. The ‘Q’ outputs of the counter are used to drive a logic circuit that gives the output shown in TABLE 1. (a) Design the counter using...

Specialization as defined in Wikipedia: "Concept B is a specialisation of concept A if and only if: every instance of concept B is also an instance of concept A; and there are instances of concept A which are not instances of concept B" We then call B as special case of A, it seems evident...

I was wondering whether or not there could be a "master formula" . What I mean by a master formula is, maybe not even a formula, some mathematical expression that would allow mathematicians to prove statements simply by plugging in some numbers into a formula. So I guess in a way a I am...

Which course do you guys think would be more interesting/helpful for a physics major? They are both 100 level, Intro consists of two lectures and a seminar a week, and Practical Logic consists of a three hour lecture once a week.

Let Q denote the theory of Robinson Arithmetic. A theory T is nice iff T is consistent, is p.r. adequate and extends Q. The fixed-point lemma states that for all nice theories T, for any formula φ, there is a sentence σ such that T ⊢σ↔φ("σ")...

Homework Statement Suppose R1 and R2 are relations on A and R1 ⊆ R2. Let S1 and S2 be the transitive closures of R1 and R2 respectively. Prove that S1 ⊆ S2. Please check my proof and please explain my mistakes. thank you for taking the time to help. Homework Equations N/A The Attempt at a...

Are undecidable statements, such as the provability of the continuum hypothesis, natural examples of statements that require a multivalent logic in order for them to be adequately described and/or even properly understood? (NB: by properly I am taking this to mean that undecidable matters such...

How to translate "there exists exactly one happy person" into predicate logic? I came up with $$ \exists x : happy(x) \implies \forall y: happy(y) \land y = x$$. But this is incorrect. I also tried $$\exists x: happy(x) \land \forall y: happy(y) \land x = y$$. This is also incorrect. The...

I'm unsure about these three, here are my attempts. Please also explain the difference between a predicate and true/false. I assumed it is a predicate when it can be either true or false. a) Predicate. Negation is ¬(∃n ∈ N n²>n) b) True. Negation is, "When x<0 there is y such that y^2=x c) No...

Homework Statement Using only NOT and XOR, construct a compound statement having the same truth table as: (a) p OR q (b) p AND q Homework Equations XOR is "exclusive OR." p XOR q = (p OR q) AND NOT (p AND q). I have been working under the assumption that I can use parentheses. The...

Hi there, I desperately need your help :P I was very ill for the past week and missed out on class time when we were taught the content. I attempted the homework questions but because I've had to breeze through the content I'm not sure if I have answered all the questions correctly or as well...

Why is it required to use a "fresh name/variable"? And because of that requirement, Existential instantiation always precedes universal instantiation. What I am thinking is, If we are picking elements at random from our universe of discourse then why can't universal instantiation pick that...

Homework Statement is my method valid? ∃x¬R(x,a) --> ¬∃R(a,x) ¬R(a,a) thus, ¬R(a,b) Homework Equations N/A The Attempt at a Solution ∃x¬R(x,a) by existential gen. of ¬R(a,a) ¬∃R(a,x) by modus ponens ∀x¬R(a,x) by identity of ¬∃R(a,x) ¬R(a,b) by universal instantiation of ∀x¬R(a,x)