Equivalence relations Definition and 58 Threads

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...

Homework Statement Let S be the set of integers. If a,b\in S, define aRb if ab\geq0. Is R an equivalence relation on S? Homework Equations The Attempt at a Solution Def: aRb=bRa \rightarrow ab=ba assume that aRb and bRc \Rightarrow aRc a=b and b=c since a=b, the substitute a...

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...

[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 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...