Relation between symmetric and asymmetric relations | Discrete Mathematics
The relationship between symmetric and asymmetric relations is that these two properties are mutually exclusive. It means that a relation cannot be both symmetric and asymmetric at the same time except R={ } . This is because symmetric relations allow for bidirectional relationships, while asymmetric relations prohibit bidirectionality and enforce a strict one-way relationship.
It is important to note that a relation can be symmetric without being asymmetric, and vice versa. For example, the relation "is a sibling of" on the set of individuals is symmetric since if person A is a sibling of person B, then person B is also a sibling of person A. However, it is not asymmetric because the relation allows for bidirectional relationships.
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