About
A symmetric relation is a type of binary relation that happens when for all a and b in X
- if a is related to b,
- then b is related to a
In mathematical notation, the relation f between x and y is symmetric when <MATH> y = f(x) \\ x= f(y) \\ </MATH>
A relation which is not symmetric is asymmetric.
A symmetric relation is an undirected relationship
A symmetric relation is also known as a bi-directional relation.
Articles Related
Example
Representation
Entity Model
When there is no direction on the association, the relationship is symmetric.
Set
A symmetric relation in the set of {1,2} would be the set of tuple
<1,2>
<2,1>
<1,1> // reflexive
<2,2> // reflexive
Visual
The relation between x and y is represented by the gray area. The relation is symmetric when <MATH> y = f(x) \\ x= f(y) \\ b = f(a) \\ a = f(b) \\ </MATH>
- Symmetric but not reflexive
- Symmetric and reflexive (because the relation y=x (the dotted line) is in the relation)
- Not symmetric (nor reflexive, nor antisymmetric)
