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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").
The 3H-model of motivation ("3H" stands for the "three components of motivation") was developed by professor Hugo M. Kehr, PhD., at UC Berkeley. [1] The 3C-model is an integrative, empirically validated theory of motivation that can be used for systematic motivation diagnosis and intervention.
A relation R is quasitransitive if, and only if, it is the disjoint union of a symmetric relation J and a transitive relation P. [2] J and P are not uniquely determined by a given R; [3] however, the P from the only-if part is minimal. [4] As a consequence, each symmetric relation is quasitransitive, and so is each transitive relation. [5]
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.
Relations that satisfy certain combinations of the above properties are particularly useful, and thus have received names by their own. Equivalence relation A relation that is reflexive, symmetric, and transitive. It is also a relation that is symmetric, transitive, and serial, since these properties imply reflexivity. Orderings: Partial order
A relation R is said to be reflexive if a R a holds for every a in the domain of the relation. Every reflexive relation on a nonempty domain has infinite descending chains, because any constant sequence is a descending chain. For example, in the natural numbers with their usual order ≤, we have 1 ≥ 1 ≥ 1 ≥ ....
A relation is connex if and only if its complement is asymmetric. A non-example is the "less than or equal" relation ≤ {\displaystyle \leq } . This is not asymmetric, because reversing for example, x ≤ x {\displaystyle x\leq x} produces x ≤ x {\displaystyle x\leq x} and both are true.
Reversal theory is a structural, phenomenological theory of personality, motivation, and emotion in the field of psychology. [1] It focuses on the dynamic qualities of normal human experience to describe how a person regularly reverses between psychological states, reflecting their motivational style, the meaning they attach to a situation at a given time, and the emotions they experience.