# Logical Data Modeling - Symmetric relationship (bi-directional)

### Table of Contents

## 1 - 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.

## 2 - Articles Related

## 3 - Example

## 4 - Representation

### 4.1 - Entity Model

When there is no direction on the association, the relationship is symmetric.

### 4.2 - 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
```

### 4.3 - 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)