Relations Definition and 540 Threads

Homework Statement T is a binary relation defined on A = {0, 1, 2, 3}. Let T = {(0,2), (1,0), (2,3), (3,1)} Find T^t, the transitive closure of T.The Attempt at a Solution I'm going to skip using commas cause it takes to long 02 23 = 03 31 10 = 30 23 31 = 21 10 02 = 12 12 23 = 13 02 21 = 01...

This is a question from A consise introduction to pure mathematics (Martin Liebeck) Hi guys, just stuck on one problem was wondering if someone could lend me hand. Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers ...

This is a question from A consise introduction to pure mathematics (Martin Liebeck) Hi guys, just stuck on one problem was wondering if someone could lend me hand. Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers ...

I'm having a course in advanced quantum mechanics, and we're using the book by Sakurai. In his definition of angular momentum he argues from what the classical generator of angular momentum is, and such he defines the generator for infitesimal rotations as...

Homework Statement Let \psi(\vec{r},t) be the wavefunction for a free particle of mass m obeying Schrodinger equation with V=0 in 3 dimensions. At t=0, the particle is in a known initial state \psi_0(\vec{r}). Using Ehrenfest's theorem, show that the expectation value <x^2> in the state...

My question goes like this: Did the inflation following the Bing Bang caused matter to emerge as it is in our universe? In other words, was it the inflation itself that gave matter - electrons, neutrons and protons - its properties (physical size, quantums, velocity, mass), or perhaps the two...

Given an element (6, 5, 4) of S (that is {(6, 5, 4)} is a subset of S); assuming S is a relation, how exactly do we donate the relations between the elements of the 3-tuple formed in this case; the relation can be of 3 sorts (in a 3-tuple) - 6S5 6S4 5S4 Out of these 3 how many relations...

Statement: Prove or Disprove: A relation ~ on a nonempty set A which is symmetric and transitive must also be reflexive. Ideas: If our relation ~ is transitive, then we know: a~b, and b~a \Rightarrow a~a. Therefore our relation ~ is reflexive, since b~c and c~b \Rightarrow b~b, and c~a...

Hello! I'm a bit lost on these questions pertaining to equivalence relations/classes. If someone could run me through either, or both, of these questions, I'd be very thankful! I'm completely lost as to what to do with the z in terms of set S... Homework Statement Show that the given...

if \mu = cos(\theta) and \mu_{0} = cos(\theta_{0}) and cos(\pi - \Theta) = \mu_{0}\mu + \sqrt{1-\mu_{0}^{2}}\sqrt{1-\mu^{2}}cos(\phi) Then cos(\pi - \Theta) = cos(\theta_{0})cos(\theta) + sin(\theta_{0})sin(\theta)cos(\phi) Is this not correct?

Hi, I would like to know if you guys know a good book on sets groups and relations, preferably with lots of exercises. I believe that I am on a beginner level, but I already know all basic concepts, so the text is not that important. It would be even better if it is available online hehe! Thks!

Homework Statement I'm working through a bit of group theory (specifically SU(2) commutation relations). I have a question a bout symmetries in the SU(2) group. It's something I'm trying to work through in my lecture notes for particle physics, but it's a bit of a mathsy question so I thought...

A relation R on R^2 is defined by (x_{1},y_{1})\mathit{R}(x_{2},y_{2})\;\;\;if\;\;\;x_{1}^{2}+y_{1}^{2}=x_{2}^{2}+y_{2}^{2} How do you show that R is an equivalance relation?

Hello :smile: I was wondering if I could get some help with work on Binary Relations. We've done very little of this in class, and hours of Googling has provided little help. So I was hoping that someone could look over my attempts at the questions and let me know if I've gone wrong...

There must something wrong with my understanding of this relations because I think the usual way they are derived in many textbooks makes no sense. It goes like this, first assume that to every rotation O(a) in euclidean space there exists a rotation operator R(a) in Hilbert space,second: the...

Hi all.. I've been seeing the famous equation which 'converts' horsepower into torque: HP = Torque (lb/ft) * rpm / 5252. The 1/5252 comes from 2*PI/33,000. Power (rotational) is simply torque * angular velocity, isn't it? When I try to plot the imperial version, I get the typical graph with HP...

In pipe flow of a viscous fluid, what happens to the head lost due to friction and "minor losses" (pipe bends, valves, etc).?I mean, if you decrease the dynamic pressure by reducing flow velocity, then the static pressure increases. If the dynamic pressure increases then the static pressure...

Homework Statement If R and S are two equivalence relations on the same set A, we define R ◦ S = {(x, z ) ∈ A × A : there exists y ∈ A such that (x, y) ∈ R and (y, z ) ∈ S }. Show that the following conditions are equivalent: (i) R ◦ S is a symmetric relation on A ; (ii) R ◦ S is a...

Homework Statement The dispersion relation for a plasma is given by k^{2}=\frac{\omega^{2}}{c^{2}}(1-\frac{\omega^{2}_{p}}{\omega^{2}})\omega^{2}_{p}\:= \frac{Ne^{2}}{m_{e}\epsilon_{0}} Where N is the electron density During re enrty of a spacecraft there was a radio blackout of all...

Homework Statement Is this relation symmetric? The relation in a set of people, "is brother of" Homework Equations aRb , bRa The Attempt at a Solution The answer is not symmetric. They gave example says that paul may be the bother of Anne but Anne is not the brother of paul...

Hello: I am asked to find a recurrence relation for the number of n letter sequences composed of A, B, C where every A that is not in the last position is followed by a B. So, would this be: A| (we have A(n-2) sequences) + 0 if A is in the last position B| we have A(n-1) C| we have...

Homework Statement In the following series': http://image.cramster.com/answer-board/image/cramster-equation-2009410014306337491927047975008434.gif According to my book, we only have a common range of summation here for n >= 2. Therefore we need to treat n = 0 and n = 1 separately...

Homework Statement Straight line segments are drawn from the fixed point P1(0,1) and P2(3,2) to the movable point P, with coordinates (x,0)on the positive x-axis. Assuming that 0 ≤ x ≤ 3, show that the angle θ between the two line segments PP1 and PP2 is given by the relation: θ=...

I was wondering- is it possible to derive an equation of motion for example, the Schrodinger equation from the uncertainty principle (in commutator form)? i.e. Is it possible to derive the Schrodinger equation from the following: \left[\hat{x},\hat{p}\right]=ih I gave it a shot, but of...

Is there a general method for solving 2-index recurrence relations with constant coefficients? Here is one I would like to solve a_{m,n} = \frac{xa_{m-1,n} + ya_{m,n-1} + 1}{x+y} for m,n > 0 with initial conditions a_{m,0} = m/x and a_{0,n} = n/y. Hoping for an analogy with...

Homework Statement Let A = {a, b, c} be a set with 3 elements. (a) How many binary relations are there on A? (b) How many binary relations on A are reflexive? (c) How many relations on A are symmetric? (d) How many binary relations on A are both symmetric and reflexive? Homework...

Homework Statement x1,x2) are the components of a 2 dimensional vector r when referred to cartesian axes along the directions i,j. derive the relations x1'= cosΘ x1+sinΘ x2 x2'=-sinΘ x1+cosΘ x2 for the components (x1',x2') or r referred to new axes i',j' obtained by a rotation of the axes...

Homework Statement Show that, [a, \hat H] = \hbar\omega, [a^+, \hat H] = -\hbar\omega Homework EquationsFor the SHO Hamiltonian \hat H = \hbar\omega(a^+a - \frac{\ 1 }{2}) with [a^+, a] = 1 [a, b] = -[b, a] The Attempt at a Solution I have tried the following: [a, \hat H] = a\hat...

Homework Statement Verify that the relation x^2 + y^2 = 1 is a solution to the differential equation: dy/dx = xy/(x^2 - 1) Can anyone point me in the right direction on how to begin to solve this problem? Do I take integral of the DE and just plug into equation?

In every textbook about analytic mechanics, it will give the relation of time derivative of some variable between the space coordinate and body coordinate \left(\dfrac{d\vec{v}}{dt}\right)_{space} = \left(\dfrac{d\vec{v}}{dt}\right)_{body} + \vec{\omega}\times\vec{v} I don't really...

Can anyone help me with this? Thank you very much Given set A={m,b,f,a,s} and B={m,b,s} a) Is {<m,s>, <b,m>, <f,m>, <a,b>} a function? Is it a relation or function from A to B, A to A, B to A, B to B or none of the above? b) Is { } a function? Is it a relation or function from A to B, A...

Homework Statement Find f(n) when n = 2^k, where f satisfies the recurrence realtion f(n) = f(n/2) +1 with f(1) = 1 Homework Equations f(n) = a*f(n/b) + c when n = b^k, where k is a positive integer, f(n) = C1n^(log a base b) + C2 C1 = f(1) +c/( a-1) and C2 = -c/ (a-1) keep in mind...

Hey guys. Right, I have been studying the Maxwell thermodynaic relations. But I have come across entropy as dS = (bS/bT)_P(dT) + (bS/bP)_T(dP) where b is the partial differential symbol. I don't understand where this comes from, which suggests S(T,P). I can't find a derivation of...

Mass is the product of density and volume. Mass flow rate is the product density, velocity, and cross-sectional area. (It's the derivative of mass with respect to time.) Bare with the syntax please... Looking at a sphere within a larger sphere, the volume of the difference is...

What is an empty relation? Can an empty relation be a function? Is an empty relation one with the empty set as its domain or as its range or both? THanks

Homework Statement On set PxP, define (m,n)\approx(p,q) if m*q=p*n Show that \approx is an equivalence relation on PxP and list three elements in equivalence class for (1,2) Homework Equations The Attempt at a Solution I will appreciate any help how to start this problem...

Almost all the explanations of quantum cryptography I've come across simply say that the encryption is "protected by the Heisenberg uncertainty principle". I'm having a little difficulty getting any more detail than that without getting way out of my depth (I'm only an A-level student!). Does...

Homework Statement http://img510.imageshack.us/img510/5505/systemet4.jpg What I wish to do is to relate the accelerations of the loop an the massive block. I know the angle theta at any instant. I also know that the acceleration of the loop on the fixed support is a. I have been given no...

Homework Statement Find relations that satisfying just Reflexive just Symmrtic just Transitive (R) & (S), but not (T) (R) & (T), but not (S) (S) & (T), but not (R) Homework Equations S=Z (a,b) \inR if <=> a>b (T) but, not (S) & (R). the ex is given in the class, but...

Homework Statement question 1: Define ~ on Z by a ~ b if and only if 3a + b is multiple of 4. question 2: Let A = {1,2,3,4,5,6} and let S = P(A) (the power set of A). For a,b \in S define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence...

Homework Statement Homework Equations [PLAIN]http://upload.wikimedia.org/math/7/7/4/7745116605c54295c6c3b696cea2d39f.png[/URL] The Attempt at a Solution I have gotten these problems wrong too many times. I know that I have to apply both the conservations of momentum and kinetic energy, but...

Find Generators and relations analogous to (2.13) for the Klein four group.? (2.13) i^4=1, i^2=j^2, ji=(i^3)j. (a) Find Generators and relations analogous to (2.13) for the Klein four group. (b) Find all subgroups of the Klein four group. Please show steps! Thank you.

Suppose X, Y, Z are sets. If X ~ Y and Y ~ Z, prove that X ~ Z. My work on the proof so far is: Suppose X, Y, Z are sets. Let X ~ Y and Y ~ Z. By equivalence, there are functions f and g such that f: X → Y where f is 1-1 and onto, and g: Y → Z where g is 1-1 and onto. So now I have to...

Homework Statement There's this one exam problem that I cannot solve... Here it goes: Consider the set Z x Z+. Let R be the relation defined by the following: for (a,b) and (c,d) in ZxZ+, (a,b) R (c,d) if and only if ad = bc, where ab is the product of the two numbers a and b. a) Prove that...

"equating" the uncertainty relations? can you write this: dEdt~dxdp and then compute with it?

Show that: \left(\frac{\partial z}{\partial y}\right)_{u} = \left(\frac{\partial z}{\partial x}\right)_{y} \left[ \left(\frac{\partial x}{\partial y}\right)_{u} - \left(\frac{\partial x}{\partial y}\right)_{z} \right] I have Euler's chain rule and "the splitter." Also the property...

The system is given in the picture. I want to know the relation between the acclerations of each block. My attempt: suppose if the body in the middle moves up by x. the string will get loose by 2x. therefore, if a1, a2, a3 are the acclerations. -2*a2=a1+a3 am i correct?

if tachyons existes, does they obey the transfomation relations similary to the relations of special relativity? that we see in discussitions about tachyons , usually relations are same by a difference in compelexility of mass and charge . but the velocity in denominator is same, here the...

I have a question... "Is the quotient set of a set S relative to a equivalence relation on S a subset of S?" I suppose "no",since the each member of the quotient set is a subset of S and consequently it is a subset of the power set of S,but I have e book saying that "yes",I am a bit...

[SOLVED] viete's relations problem Homework Statement The zeros of the polynomial P(x) = x^3 -10x+11 are u,v,and w. Determine the value of arctan u +arctan v+ arctan w.Homework Equations http://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formulas The Attempt at a Solution I must admit I have no idea...