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
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...
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...
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...