Hey all, I was wondering if anyone could shed some light on this question.
Let X= {1,2,3,4,5} and Y={3,4}
b) What is the equivalence class of {1,2}?
I understand equivalence relations but can't seem to grasp the concept of equivalence classes. :|
Any explainations would be appreciated. Thanks in advance!
That bit of a question makes no sense whatsoever.
Please post the entire question with its exact wording.
Apologies.
Let X = {1,2,3,4,5} and Y = {3,4}.
Define a relation R on the power set P(X) of X by A R B iff A U Y = B U Y.
a) Prove that R is an equivalence relation.
b) What is the equivalence class of {1,2}?
Firstly, so for all .
Suppose and . Then . So, by symmetry and transitivity of usual set equality, and So it's an equivalence relation.
For b, what is the equivalence class of is asking what things are R-related to A. If B is R-related to A, then . Then clearly, as 1 and 2 aren't members of Y, we can conclude that and furthermore, 3 or 4 could be on B (that wouldn't effect anything since they would be in their after unioned with Y anyway). So it's equivalence class is