What is the difference between asymmetric and antisymmetric

Anti symmetric? Same goes for irreflexive and anti-reflexive. From my understanding, it is irreflexive if for no x then x,x. But what if you have only one element that refers to itself? According to your "rewritten" condition, for every couple of individuals, we have that the first one is father of the second and the second is not father of the first one, which sound quite unreasonable.

Every asymmetric relation is also antisymmetric. But if antisymmetric relation contains pair of the form a,a then it cannot be asymmetric. It can be reflexive, but it can't be symmetric for two distinct elements. Asymmetric is the same except it also can't be reflexive. So an asymmetric relation is just one that is both antisymmetric and irreflexive. So in matrix representation of the asymmetric relation, diagonal is all 0s. And in digraph representation , there are no self-loops. If you make a set of all type 2 people and they may be Sane or Insane people.

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Akash Mittal answered Nov 18, A relation is asymmetric if and only if it is both antisymmetric and irreflexive. A transitive relation is asymmetric if and only if it is irreflexive.

Mk Utkarsh answered Mar 31, Next Qn. Related questions 0 votes. Ayush Upadhyaya asked in Mathematical Logic Dec 25, My Work: Whose Size is maximum means, we should take all reflexive pairs. We can have Please guide me to the correct thought process. Set Theory. Graph Theory. Linear Algebra. Math Practice Questions. Table of Contents. Save Article. Improve Article. Like Article. Previous Mathematics Algebraic Structure. Next Discrete Mathematics Representing Relations.