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This is not asymmetric, because reversing for example, produces and both are true. The less-than-or-equal relation is an example of a relation that is neither symmetric nor asymmetric, showing that asymmetry is not the same thing as "not symmetric".
Symmetric and antisymmetric relations. By definition, a nonempty relation cannot be both symmetric and asymmetric (where if a is related to b, then b cannot be related to a (in the same way)). However, a relation can be neither symmetric nor asymmetric, which is the case for "is less than or equal to" and "preys on").
A relation can be both symmetric and antisymmetric (in this case, it must be coreflexive), and there are relations which are neither symmetric nor antisymmetric (for example, the "preys on" relation on biological species). Antisymmetry is different from asymmetry: a relation is asymmetric if and only if it is antisymmetric and irreflexive.
Symmetrical interactions send the moral message "we are all the same" while asymmetrical interactions may send the message "I am special; better than you." Peer relationships, such as can be governed by the Golden Rule, are based on symmetry, whereas power relationships are based on asymmetry. [35]
For example, > is an asymmetric relation, but ≥ is not. Again, the previous 3 alternatives are far from being exhaustive; as an example over the natural numbers, the relation xRy defined by x > 2 is neither symmetric (e.g. 5R1, but not 1R5) nor antisymmetric (e.g. 6R4, but also 4R6), let alone asymmetric. Transitive
That means, that individuals of a species can be symmetric, or even asymmetric to the opposite side (see, e.g., handedness), but most individuals are asymmetric to the same side. The relation between directional and fluctuating asymmetry is comparable to the concepts of accuracy and precision in empirical measurements.
In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets {,,} and {,} is {,,}.
A reflexive and symmetric relation is a dependency relation (if finite), and a tolerance relation if infinite. A preorder is reflexive and transitive. A congruence relation is an equivalence relation whose domain X {\displaystyle X} is also the underlying set for an algebraic structure , and which respects the additional structure.