say we have a set W. We also have a non-empty set Z such that each element of Z is an equivalence relation on W.
Must show that the nZ is an ER in W. (where n is intersection)
how would this be proven, like i know that u must prove that it is reflexive, transitive and symmetric but how exactly would u start it?
my question is
let W be a set.
Let Z be a non empty set such that each element of Z is an equivalence relation on W
i must show that the nZ is an equivalence relation on W. (where nZ is the intersection of Z)
how would i go about proving this is true?
i understand that i have to prove that the relation is reflexive, anti-symmetric and transitive, but how would i do that
Ok, now that I think about it I believe that I understand what this is saying. if is an equivalence relation on then is charcterized by . Maybe that if we consider the different relations on to be charchertized by (not necessarily countable..I just wrote it that way for clarity) then perhaps they mean to show that is an the characterization of an equivalence relation. Does that sound right? Another member may swoop in an answer this btw.
The gist of the problem is to prove the following. Let be a set and let and be relations (i.e., subsets of ) on . Moreover, suppose that and are equivalence relations. Show that is an equivalence relation a well.
(This solves the problem when the set of equivalence relations has size 2, or, in fact, any finite size. To be strict, one has to prove this also for infinite , but the proof is essentially the same.)
This should be easy to show by definition.