Define a reflexive relation.

Explanation

To define a reflexive relation, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Set**:
- Let's consider a set \( A \). For example, let \( A = \{ a, b \} \).

2. **Defining a Relation**:
- A relation \( R \) on set \( A \) is a subset of the Cartesian product \( A \times A \). This means that \( R \) consists of ordered pairs where both elements come from set \( A \).

3. **Condition for Reflexivity**:
- A relation \( R \) is called reflexive if every element in the set \( A \) is related to itself. This means that for every element \( x \) in \( A \), the pair \( (x, x) \) must be in the relation \( R \).

4. **Example of a Reflexive Relation**:
- For the set \( A = \{ a, b \} \), a reflexive relation \( R \) would include the pairs \( (a, a) \), \( (b, b) \). Thus, \( R = \{ (a, a), (b, b) \} \) is reflexive.

5. **Conclusion**:
- Therefore, a relation \( R \) on set \( A \) is reflexive if it contains all pairs of the form \( (x, x) \) for every \( x \) in \( A \).

### Final Definition:
A relation \( R \) on a set \( A \) is called reflexive if for every element \( x \in A \), the pair \( (x, x) \) is in \( R \).

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