0 votes 0 votes is empty relation R={ } on en empty set A={ } is equivalence? Set Theory & Algebra discrete-mathematics + – namvar asked Jul 29, 2018 namvar 543 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Shubham Shukla 6 commented Jul 29, 2018 reply Follow Share I think it should be in equivalence.! empty relation is by default transitive and symmetric, just you need to check for reflexive as here no element in set, so empty relation would be reflexive..:) so its an equivalence relation. correct me if i am.wrong.! 4 votes 4 votes namvar commented Jul 29, 2018 i reshown by namvar Jul 29, 2018 reply Follow Share This relation can be reflexive as well as irreflexive but the intersection of both is null then it is hard to say it is reflexive or irreflexive. And also the definition of relations is for non empty sets not for empty set 0 votes 0 votes Shubham Shukla 6 commented Jul 29, 2018 i edited by Shubham Shukla 6 Jul 29, 2018 reply Follow Share @nemvar no.i dnn think you are correct please see this image. https://math.stackexchange.com/questions/690482/is-the-relation-r-emptyset-is-it-reflexive-symmetric-and-transitive-why 2 votes 2 votes Please log in or register to add a comment.