Symmetric Relation -- from Wolfram MathWorld
Symmetry, and Transitivity. • Definition: Let R be a binary relation on A. • R is reflexive if for all x ∈ A, (x,x) ∈ R. (Equivalently, for all x e A, x R x.) • R is symmetric. Contents. [hide]. 1 Definition. Symmetric; Asymmetric; Antisymmetric; Non-symmetric. 2 Linguistic Note; 3 Also see. Is (−35) L 1? • N-ary Relations – A relation defined on several sets. Symmetric: If any one element is related to any other element, then the second element is.
They applied those observations to psychology, suggesting that as people in families communicate with each other, they respond in similar feedback loops. This leads the first person or group to react to those reactions and so forth in an endless communication loop. When pursuers feel there is too much space between them and a partner, they pursue.
If the distancers feel they are being crowded, they distance in order to get some space.
If the distancer distances too much, the pursuer again pursues. To describe their new understanding of family dynamics, they adopted the term cybernetics. Symmetrical — where people respond to each other in similar ways and Complementary — where one person yields to or supports the other.
When expressed in healthy ways, either type of feedback loop results in growth and positive change.
But, if not checked by cultural norms or positive values, the communication loop can get out of control and become unhealthy and destructive. The team went on to more clearly specify healthy as well as unhealthy ways that symmetrical or complementary relationships can work. In healthy symmetrical relationships, the two parties mirror each other. An unhealthy example of symmetry would be of two siblings who are brutally competitive with each other.
Neither can rest in their anxiety to always be on top. Each spends his life anxiously looking over his shoulder to see whether his brother is besting him and renewing his own efforts to be best and first.
Symmetric relation - Wikipedia
An unhealthy complementarity can be seen in couples where one person dominates disrespects and controls the other and the other person responds by becoming more and more passively the victim. For a more thorough explanation of these communication patterns, see Watzlawick, Beavin and Jackson, Pragmatics of Human Communication: Their experimental and innovative work forms the basis of much of what we do in family therapy today.
Because the work at Palo Alto was a seismic shift in thinking. Treatment necessarily then moved from treating each individual to treating the communication within the system as a whole. These relationships generally develop because it is felt — either consciously or unconsciously — that such similarities are important in the process of developing relatedness, mutuality, bondedness, stability and so forth.
Symmetric Relation on Set | Solved Example of Symmetric Relation
There are certainly beneficial elements of symmetrical relationships. Some important areas of similarity or agreement typically translate to better marital adjustment and satisfaction. Such areas are often related to having similar backgrounds and life experiences. They include moral values, religious beliefs and affiliation, political ideology, views on family, and others.
This does not mean that marriages which are not in perfect agreement in all of these areas are necessarily doomed for failure. But, those who enjoy harmony in most or all of these areas are generally at an advantage.
Common interests often result in shared activities which can help to develop intimacy and friendship in relationships. These are a couple of the other benefits of symmetrical unions.
The symmetrical style of relationship is not without potential problems, however. When commonality is viewed as extremely important to one or both spouses and the relationship is based, to a great degree, on this understanding then certain expectations naturally develop. When differences come to the surface — which is inevitable since no two people are identical in every way — it can be a disappointing experience.