Relations Definition and 540 Threads

Homework Statement let A be any set of numbers and let R and S be relations on A. if S and R are symmetric then show S o R is symmetric. if S and R are antisymmetric then show S o R is antisymmetric. if S and R are transitive then show S o R is transitive. if S and R are...

Homework Statement For each of the relations on the set R x R - (0,0) (ie. no origin) : - prove it is an equivalence - give the # of equivalence cases - give a geometric interpretation of the equivalence cases assuming an element of R x R is a point on a plane a) {((a,b),(c,d)) |...

I know how to solve second order ones, but how would you solve third order ones? Because the characteristic polynomial would have a third degree so how can one find the roots? I have looked everywhere online to find out but I can't find anything. Please Please tell me!

Would be really grateful if someone helped me with 5a, and explained the ideas behind recursion relations. I don't know what a recursion relation is, and how to apply for forum ales given Homework Statement http://img839.imageshack.us/img839/2301/recurrencerelation.gif...

Homework Statement Provide an example that shows why the reflexive property is not redundant in determining whether a relation is an equivalence relation or not. For example, why can't you just say, "If xRy then yRx by symmetric property, and then using transitive property you get xRx."...

Homework Statement Assuming V is a function of P and T such that V = V(P,T) express the differential changes in volume due to differential changes in Temperature and pressure, what is the fractional/relative change? Homework Equations The Attempt at a Solution since V is a...

Homework Statement Verify the following commutation relations using \vec J = \vec Q \times \vec p and [Q_{\alpha},p_{\beta}]=i \delta_{\alpha \beta} I 1. [J_{\alpha}, J_{\beta}]=i \epsilon_{\alpha \beta \gamma} J_{\gamma} 2. [J_{\alpha}, p_{\beta}]=i \epsilon_{\alpha \beta \gamma}...

From the wikipedia page on http://en.wikipedia.org/wiki/Complementarity_(physics)" : As I recently noticed in the double-slit experiment there is a lot of time-uncertainty, not only position-momentum uncertainty. That is shown in the fact that the probability wave does not reach the screen...

Homework Statement Solve the Mass-Spring-Damper Differential equation mx''+bx'+kx=exp(-t)cos(t) (Where x'' is d2x/dt2 etc, don't know how to do the dots above :confused:) I understand how to solve this problem, but the thing that confuses me is that the right is in terms of "t"...

Homework Statement The set A has 5 elements. 1. How many relations exist on A? 2. How many of those relations are symmetric and reflexive? The Attempt at a Solution Some of the parts of this question are harder than others. 1. By simple counting, there are 2^(5^2) or 2^25 total relations...

Homework Statement I am not an expertize at algebra, and recently I was considering derivisions of equations based on postulates already known to physics. I just wanted a little guidence if any of the equations are inconsistent, which I am sure probably quite a few are, knowing my own...

My professor did this in lecture, and I can't figure out his logic. Can someone fill in the gaps? He went from: dS = \left( \frac{\partial S}{\partial P} \right)_T dP + \left( \frac{\partial S}{\partial T} \right)_P dT (which I totally understand; it just follows from the fact that...

I have two questions: i) Does a distinct equivalence relation on a set produce only one possible partition of that set? ii) Can multiple (distinct) equivalence relations on a set produce the same partition of that set? In other words, given a set S and two distinct equivalence relations ~...

The relation to be proved looks pretty simple. However, there is no evident point from whih I can start. How do I start relating quantities that are under root? The cyclic order of the sides on the left side is reminiscent of the cosine rule, but that's just it! Plus the right hand side...

Homework Statement We propose to study simple processes of liquid alcohol. At T_1, the molar volume of alcohol is V_1 and its molar heat capacity at constant pressure is C_p,m. We assume that its isobaric coefficent of thermal expansion a, and the isothermal compressibilty coefficient B are...

Homework Statement Given is the set X. The set of functions from X to [0,1] we call Fun(X,[0,1]). On this set we consider the relation R. An ordered pair (f,g) belongs to R when f^{-1}(0)\setminus g^{-1}(0) is a countable set. a) Prove that R is transitive. b) Is R an equivalence relation...

Can we always calculate the commutation relations of two observables? If so, what’s the commutator of P (momentum) and H (Hamiltonian) in infinite square well, considering that the momentum is not a conserved quantity?

Really struggling with this question guys, any help/advice will be greatly appreciated. Thanks in advance! Homework Statement Sketch dispersion relations for, (i) a proton (ii) a free electron (iii) an electron, in a crystalline solid. Comment on the similarities between (ii) and...

I mentioned in a thread on here almost a year ago now that I was considering making a change into math, after entertaining several other options and figuring out that I really enjoy math, and especially probabilty, I have decided to to move toward getting either another bachelor or a masters in...

Homework Statement Show that {x_i, x_j} = 2*y_ij* I for i = 1; 2; 3 and j = 1; 2; 3. where y_ij: N x N -> {0,1}, such that y_ij = {1, if i = j ; 0, if i not = j Homework Equations The Attempt at a Solution I'm confused about exactly what I'm supposed to do here. Do i do all the...

I have a complicated recursion replation, which I'm sure is unsolvable. (By "unsolvable" I mean that there is no closed form solution expressing \xi_1, \xi_2, \xi_3, etc. in terms of \xi_0.) It goes \frac{(k+4)!}{k!}\xi_{k+4} +K_1 (k+2)(k+1)\xi_{k+2}+ [ K_2 k(k-1) +K_3] \xi_{k} +K_4...

I'm really puzzled about this one. Say you have a discrete, nonnegative random variable N where the probability pn = P{N=n} satisfies the recurrence relation p_{n+2} + r p_{n+1} + s p_n = 0 for n = 0, 1, 2, ...; p0 and p1 are given. How do you find the expectation E[N] without solving...

I have a quick question about the relationship between the complex Fourier coefficient,\alpha_n and the real Fourier coefficients, a_n and b_n. Given a real-valued function, I could just find the real coefficients and plug them into the relation below, right?Fourier Coefficients for periodic...

Some books begin QM by postulating the Schrodinger equation, and arrive at the rest. Some books begin QM by postulating the commutator relations, and arrive at the rest. Which do you feel is more valid? Or are both equally valid? Is one more physical/mathematical than the other? I...

We have a equivalence relation on [0,1] × [0,1] by letting (x_0, y_0) ~ (x_1, y_1) if and only if x_0 = x_1 > 0... then how do we show that X\ ~is not a Hausdorff space ?

Hi. Let A = 1,2,3,4,5,6,7 How many symmetric relations on A contain exactly (a) four ordered pairs, (b) 5 , (c) seven and (d) eight The book has solutions to the first two, which I didn't understand at all. Please look the pic below Can someone guide me through how to approach the problem...

Homework Statement Homework Equations We're using generating functions, and recurrence relations of homogeneous and non-homogeneous types The mark allocation is 2, 3, 3 and 2 The Attempt at a Solution I think I've done the first part correctly. The closed form is in terms...

A={1,3,5} B={4,6,8,10} The set AXB that we have been using had 4096 subsets. Why? Can you find a general procedure for calculating the number of possible relations where there are k ordered pairs available? I don't know how to calculate how many relations there are? The only information I...

x,y,z\in\mathbb{R} x\sim y iff. x-y\in\mathbb{Q} Prove this is an equivalence relation. Reflexive: a\sim a a-a=0; however, does 0\in\mathbb{Q}? I was under the impression 0\notin\mathbb{Q} Symmetric: a\sim b, then b\sim a Since a,b\sim\mathbb{Q}, then a and b can expressed as...

1) Recall that an equivalence relation S on set R ( R being the reals) is a subset of R x R such that (a) For every x belonging to R (x,x) belongs to S (b) If (x,y) belongs to S, then (y,x) belongs to S (c) If (x,y) belongs to S and (y,z) belongs to S then (x,z) belongs to S What is the...

Homework Statement Starting from one of the more familiar Heisenberg Uncertainty Relations, derive the Uncertainty Relation involving angular momentum and angular displacement and explain its significance. Homework Equations The relevant uncertainty relationship is that between...

I'm having trouble with number three. I know Viete's relations are X1+X2+X3, X1X2+X1X3+X2X3, and x1x2x3 for a cubic equation.

I am having trouble understanding a basic problem in fluids that came up during an exam I took last quarter. Namely, we are given a dispersion relation and asked to quantify how a one dimensional surface disturbance propagates in space. (The disturbance is initially an approximate delta function...

I am aware that the commutation relation between conjugate variables shows that one quantity is the Fourier transform of the other, and so to imply the Heisenberg Uncertainty condition. So for example, the commutation relation between x, p (position and momentum respectively) leads to a non-zero...

Homework Statement Suppose r and s are two positive real numbers. Let Dr and Ds be defined as in part 3 of Example 4.3.1. What is D_r \circ D_s? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.) Homework Equations Example 4.3.1...

Hi guys, I'm looking for some references where dispersion relations, say for photons, are explicitely written out in a generic medium. In other words, the dispersion relation for particles not propagating in the vacuum is a different one than the standard vacuum one E^2 = p^2 + m^2 and I'm...

Hello, I am looking for a formal way to represent an n-ary relation as a combination of binary relations and logical connectives. Suppose we have a set A, a set B = \{b: b\subseteq A^2\} of binary relations over A, and a set of logical connectives C = \{\neg, \wedge, \vee\}. We define a set...

Homework Statement I have got myself very confused about equivalence relations. I have to determine whether certain relations R are equivalence relations (and if they are describe the partition into equivalence classes, but I'll worry about that once I understand the first part). Here are...

Homework Statement I need a little help in understand this question: Let E and F be two sets, R a binary relation on the set E and S a binary relation on the set F. We define a binary relation, denoted RxS, on the set ExF in the following way ("coordinate- wise"): (a,b) (RxS) (c,d) <-->...

Hey! Hoping you guys could help me with a small issue. No matter how hard I try, I don't seem to fully understand the notion of an equivalence relation, and henceforth an equivalence class. What I do understand that, in order to have and equivalence relation, it is defined to satisfy three...

I wasn't sure whether to post this in the algebra forum or here, but it seems that this is more of a logic question so I'm going with here. I am trying to understand whether there is a difference between the following two definitions of an equivalence relation: Definition 1: A binary relation...

Heisenberg's uncertainty relations are not covariant under Lorentz transformation. That means they don't have the same form in any inertial frame. So, how to modify these relations to leave them invariant in form under a Lorentz transformation ?

Homework Statement List all the functions from {1,2,3} to {1,2} representing each function as an arrow diagram. Which of these functions are (a) injective, (b) surjective, (c) bijective? For each surjective function write down a right inverse. Homework Equations The Attempt at a...

Hi, I am in grade 10 and for my final project, I am writing a report on hydrogen cars. We need to relate hydrogen cars to chemistry, ecology, climate change, and light and geometric optics. Can someone tell me how hydrogen powered cars relate to each of these? I am really unsure and need...

1. R on the set (the reals) defined by xRy iff (x < 0) or (x > or equal to 0 and x = y) 2. None 3. Reflexive - Yes, since no matter what x I choose, x will always be equal to x, and will therefore fit the conditions of the relation. Symmetric - It is symmetric because if I...

1. The question is: P on the set, A, of all people, where xPy means x is a parent of y. Homework Equations - None 3. Attempts at a Solution Here is where I am confused. Reflexivity is defined by aRa. So I am unclear what to do with more than one variable. So in this question, do I...

I have a question about a confusing section of the NESC (not that many sections are not confusing, but this is my current issue). Section 220.B.2.b reads as follows That the supply circuits be placed on the end and adjacent pins of the lowest through signal support arm and that a 750 mm (30...

How many transitive binary relations are there on a finite set of size n?

Why is there a difference when calculating pressure temperature and volume using the combined gas law, or when using adiabatic relations? As an idiot I am very confused. Why must I use a very similar equation to calculate the final temperature of an ideal gas but resulting in very different...

Hello, There are no incertitude relations in QFT. On the other hand, these incertainty relations do exist in non-relativistic QM. How can we reconcile these two facts ? Is it possible to "derive" uncertainty relations from QFT by "taking the non-relativistic limit" ? Thanks !