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
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.