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 Nov17 comment Reflexive Transitive Closure @BrianScott Why isn't a covering relation generally transitive; why isn't it ever reflexive? Nov17 comment Reflexive Transitive Closure What do you mean by this, "If $R$ is already reflexive and transitive, then $R$ is its own reflexive transitive closure, but that’s not the case with your covering relations." A covering relation isn't transitive or reflexive? Nov17 accepted Establishing A Covering Relation Nov16 asked Reflexive Transitive Closure Nov16 comment Establishing A Covering Relation No, I mean, why can't it be that $(\{a,b\},\{a,b,c\}$ is not in the covering relation, and $(\{a\},\{a,b,c\}$ is? Nov16 comment Establishing A Covering Relation Also, the answer key says that $(\{a\},\{a,b,c\}$ won't be in there, but $(\{a,b\},\{a,b,c\}$. Why couldn't it be the other way around? Nov16 revised Establishing A Covering Relation added 714 characters in body Nov16 comment Establishing A Covering Relation @ThomasAndrews My question is, why does it have to be a proper subset? I edited my post to include the description my book gives on Covering relations. Nov16 asked Establishing A Covering Relation Nov16 asked Constructing A Hasse Diagram Using The Covering Relation Nov16 accepted Definition Of Lexicographic Ordering Nov16 asked Equivalence Notation Nov15 accepted Maximal and Minimal Elements Nov15 accepted Disjoint Equivalence Nov15 asked Definition Of Lexicographic Ordering Nov15 comment Dual Of A Poset Shouldn't it be that $x=ny$? Because $x|y$ is equivalent to $y=nx$, then taking the inverse of that would be $x=ny$, which is equivalent to$y|x$ Nov15 accepted Incomparable Elements In A Poset Nov15 comment Incomparable Elements In A Poset Oh, so the relation only gives the type of condition we are looking at when we take the cross product of the powerset? We don't actually look at elements in the relation? Nov15 asked Incomparable Elements In A Poset Nov14 accepted Dual Of A Poset