I am having trouble finding examples of transitive closure of relations that are not an equivalence relation.
Asked
Active
Viewed 701 times
-3
-
I'm voting to close this question as off-topic because it's about pure mathematics and is therefore a better fit at math.stackexchange.com. – templatetypedef Aug 03 '17 at 18:17
-
I'm voting to close this question as off-topic because it is about [math.se] instead of programming or software development. – Pang Aug 05 '17 at 02:27
-
I'm voting to close this question as off-topic because it is not about programming. – Stop harming Monica Jun 19 '19 at 18:23
1 Answers
1
Any transitive relation is it's own transitive closure, so just think of small transitive relations to try to get a counterexample. Let your set be {a,b,c} with relations{(a,b),(b,c),(a,c)}. This relation is transitive, but because the relations like (a,a) are excluded, it's not an equivalence relation.
Even more trivial if you start with any nonempty set and define the empty relation on it, that relation is vacuously transitive, and even vacuously symmetric, but not an equivalence relation because you are missing the relations that would make it reflexive.
Mike Pierce
- 1,390
- 1
- 12
- 35