Relations Definition and 540 Threads

Relations Again :( K, so I am studying for the upcoming midterm... and their is this question in the book... Let A = {a} and B = {1,2,3}. List all the possible relations between A and B. So Ordered pairs, Cartesian Products and Relations are all together in the chapter, and I am really...

ok i don't know why i can't grasp this and i feel so stupid... here's an example in the book which i do get... Let S denote the set of all nonempty subsets of {1, 2, 3, 4, 5}, and define a R b to mean that a \cap b not equal to \emptyset. The R is clearly reflexive and symmetric...

R = the real numbers A = R x R; (x,y) \equiv (x_1,y_1) means that x^2 + y^2 = x_1^2 + y_1^2; B= {x is in R | x>= 0 } Find a well defined bijection sigma : A_\equiv -> B like the last problem, I just can't seem to find the right way to solve this??

Z = all integers A = Z; m is related to n, means that m^2 - n^2 is even; B = {0,1} I already proved that this is a equivalence relation, but i just don't know how to; I need to find a well defined bejection sigma : A_= -> B I hope this makes sense.. i wrote it up as well as I...

I'm doing this problem in the book - their are 2 of this kind and they have no answers in the back.. so i thought ill post one. Let S be the Cartesian coodinate plane R x R and define a relation R on S by (a,b)R(c,d) iff a+d=b+c. Verify that R is an equivalence relation and describe the...

The antisymmetric relations on a set {a,b} are those, which do not contain both of the pairs (a,b) and (b,a) because that would imply a = b, however a can't equal b since they are elements of a set? PS: In our course we allow only one copy of an element in a set, so {a,b} is a set only if a...

I answered this wrong on a test, but now I've come up with a different solution. Problem: Prove that a relation xRy\Leftrightarrow x-y\in\mathbb{Z} defined on \mathbb{R} is an equivalence relation. Solution: 1.) Reflexivity: xRx,\forall x\in\mathbb{R} For every x we have x-x=0 which is an...

Ok I'm giving these another go. I found the following DE from a reduction of order problem and figured that it would be an alright question if I turned it into one requiring a series solution. However I'm stuck. I think it's just a matter of index shifts to get an appropriate recurrence relation...

Can anyone just check if I got it right please? And if so could you just explain the theorems that come with each line? Many many thanks in advance :smile: (A-B) n (B-A) = (AuB’) n (BuA’) = (Au(BuA’)) u(B’n (BuA’)) = ((AnB) u (AnA’)) u ((B’nB) u (B’nA’)) = (AnB) u Ø u Ø u (B’nA’) =...

Let AxB be the set of ordered pairs (a,b) where a and b belong to the set of natural numbers N. A relation p: AxB -> AxB is defined by: (a,b)p(c,d) <-> a+d = b+c (i) Is (2,6) related to (4,8)? Give three ordered pairs which are related to (2,6) ANSWER: Yes (2,6)p(4,8) as 2+8 = 6+4 =...

What are the conditons on A, B and C for (AuB)nC = Au(BnC) ? Is it that AnBnC ? Can someone explain if they are different and why? :confused: Now If A = {irrationals}, B= {integers} and C={reals} does the equality from above hold in this case? I answered yes the equality holds as...

If A is the set of even integers and B the set of integers which are multiples of 3, describe the set (AUB) - (AnB) ? Basically the answer only requires words, no Venn diagram or the lot. So I just put in words ... it's the set which comprises of the even integers OR the odd integer which...

MY WORK FOLLOWS BELOW THE QUESTIONS Let AxB be the set of ordered pairs (a,b) where a and b belong to the set of natural numbers N. A relation p: AxB ----> AxB is defined by: (a,b)p(c,d) <-----> a+d = b+c As p is an equivalence relation there are associated equivalence classes. (iv)...

MY WORK FOLLOWS BELOW THE QUESTIONS Let AxB be the set of ordered pairs (a,b) where a and b belong to the set of natural numbers N. A relation p: AxB ----> AxB is defined by: (a,b)p(c,d) <-----> a+d = b+c As p is an equivalence relation there are associated equivalence classes. (iv)...

"Determine whether each of the following functions is a linear transformation. If you think the function is a linear transformation then prove that it is. If you think the function is not a linear transformation then explain why. (a) T : R2 ! R2; T(x, y) = (x − 2y, 2xy)." I don't want an...

[FONT=Verdana]Hi All I have a problem with Set theory. I am given to prove the following; Is the intersection of two equivalence relations itself an equivalance relation? If so , how would you characterize the equivalnce sets of the intersection? Regards, Nisha.

I was wondering if anyone knows where i can find the work relations for an ideal gas including isometric, isothermal, polytropic, isobaric, etc.

Hey everyone, I'm working through the first chapter of Mendelson's Topology right now and ran into this question: Let P be a subset of real numbers R such that i) 1 is in P, 2) if a,b are in P then a+b are in P, and 3) for each x in R, either x is in P, x=0, or -x is in P. Define Q=...

I originally concieved this idea whilst thinking of the UK support of Iraq war - I believe it is completely justified - although when speaking to others I was having to think of counter arguments to 'justify' the conflict and i began to think about EU/US relations and the possible effect a...

I'm following a derivation (p85 of Symmetry Principles in Quantum Physics by Fonda & Ghirardi, for anyone who has it) in which the following assertion is made: "...we have \left[\mathcal{G}_p,\mathbf{r}_i\right] &=& \mathbf{v}_0t\mathcal{G}_p, \left[\mathcal{G}_r,\mathbf{p}_i\right] &=&...

Isarel is made of Jews and US is made up of Christians but aren't Jews and Christians supposed to be enemies? How come the US and Isarel are so chummy?

The idea An epicycloid is a superimposed circle on another circle. http://www.math.dartmouth.edu/~dlittle/java/SpiroGraph/ can you find a java applet to show you. These epicycloids are tied to each other at their circumferences. But, what does change when using a slightly easier method, and...

Not really understanding these concepts. Consider the following relation on the set of all circles in the xy plane: A ~ B if and only if the center of circle A is inside circle B. Is ~ reflexive? Is ~ symmetric? Is ~ antisymmetric? Is ~ transitive? Prove answers. Consider the...

I just recently learned the Maxwell Relations in Thermodynamics. We aren't really doing anything with them, just went through the derivations. In deriving them, we started with the equation of state: TdS=dU+PdV where T is temperature, S entropy, U internal energy, P pressure, V volume. We...

I'm trying to prove the following by contradiction: [(A^B)-(B^C)]-(A^C)'=0. A, B, C are sets. All I know is in order to prove by contradiction you simply set the above not equal to zero. But I don't know where to go from there. "^" means the intersection symbol.

Hello all Show that the equality signs in Schwarz's Inequality holds if, and only if, the a's and b's are proportional; that is; ca_{v} + db_{v} = 0 for all v's where c and d are independent of v and not both zero. How would I even begin this? I know Schwarz's Inequality is: (a_1b_1 +...

So here are my questions If z(w)= R + iw/c, then 1/z = 1/(R + iw/c) Where does 1/z have singularities? I mean, there doesn't appear to be a point where R= -iw/c since R is real and the other term is imaginary. And how do I show the Real and Imaginary parts of 1/z are related by...

For some reason I am having a hard time dealing with partial order relations. The definition is what is killing me here. I have a digraph of a partial order relation and yet it does not appear to agree with the definition of partial order. I wish I could draw a picture of the digraph but since...

What are everyones thoughts on this issue? The Bush Administration wants to disallow Canadian perscription drugs to make American drug companies more profitable - or atleast "check" all Canadian drugs before they enter the States. Canada has a national health care system. Wouldn't it save...

can someone help me a) for each set of data, calculate the first differences and identify the linear and nonlinear relations b) for the nonlinear relations determine the second differences and identify the quadratic relations 1) x 5 6 8 11 y -2 -3 -5 -8...

Hi... 1. so can i say that a recurrence relation is a description of the operation(s) involved in a sequence...?... 2. is the formula for an arithmetic sequence, a recurrence relation...?... and is the formula for a geometric sequence, a recurrence relation...?...

I need to show that the solution of a_n = c_1a_{n-1} + c_2a_{n-2} + f(n) (1) is of the form U_n = V_n + g(n) (2) where V_n is the solution of a 2. order linear homogenous recurrence relation with constant coefficients. Could I use the argument that if (2) is a solution...

May I Ask This Question ... Please ... There is many sizes of Arc Welding Wires ... ( 1.5 ) , ( 2 ) , ( 2.5 ) ... etc. On what depend exactly the use of each size ... ? There is also on the Welding Machines a Volatge Controller ... for increasing or decreasing the welding voltage ...

Does anyone know of any tables that show the commutation relations of all QM opeartors? Any information would be appreciated.

How do you... Draw the graph of y=3x-2 on the grid. Identify at least two points on the graph by their coordinate pairs. Anybody get that?? It's one of those x,y axis grid thingers. And there's a table under it with 8 columns and 2 rows. Kinda like...

Question, List the members of the equivalance relation on {1,2,3,4,5} by the given partition. Identify the equivalance classes A) {(1,2,3),(4,5)} B) {(1),(2,4),(5,3)} My solution is; A) {(1,1),(1,2),(1,3),(2,2),(2,1),(2,3),(3,1),(3,2),(3,3),(4,4),(4,5),(5,4),(5,5)} B)...

I am not exactly clear on what an equivalence relation. If A is a set, then a relation on A is a subset R. The relation R is an equivalence relation on A if it satisfies the reflexive property, symmetric property, and transitive property. What types of relations are we talking about. And when...

Hello, I have a question regarding equivalence relations from my ring theory course. Question: Which of the following are equivalence relations? e) "is a subset of" (note that this is not a proper subset) for the set of sets S = {A,B,C...}. Example: A "is a subset of" B. Now...

what are all the functions f that satisfy the following relations that you can think of? \lim_{x\rightarrow \infty}\frac{f\left( x\right) }{2^{x}}=0 \lim_{x\rightarrow \infty}\frac{x^{n}}{f\left( x\right) }=0 for all n\in N.

*edited for violation of PF guidelines* What do the intelligent readers of PF think about Mexican-American relations. Let's face the fact. The real reason why Californians are ousting Gov. Davis is because of their views on how the termination of Proposition 187 affected the economy of...