Let R be a reflexive relation on a finite set A having n elements, and let there be m ordered pairs in R. Then

Options

A. `mgen`
B. `mlen`
C. `m=n`
D. none of these

Answer

To solve the problem, we need to understand the properties of a reflexive relation on a finite set.

### Step-by-Step Solution:

1. **Understanding Reflexive Relation**:
A relation \( R \) on a set \( A \) is called reflexive if every element in \( A \) is related to itself. This means that for every element \( a \in A \), the ordered pair \( (a, a) \) must be in \( R \).

2. **Identifying Elements in Set A**:
Let \( A \) be a finite set with \( n \) elements. Therefore, the elements of \( A \) can be represented as \( A = \{a_1, a_2, \ldots, a_n\} \).

3. **Counting Required Ordered Pairs**:
Since \( R \) is reflexive, it must contain the pairs \( (a_1, a_1), (a_2, a_2), \ldots, (a_n, a_n) \). This gives us a minimum of \( n \) ordered pairs that must be included in \( R \).

4. **Understanding the Given Ordered Pairs**:
We are given that there are \( m \) ordered pairs in \( R \). For \( R \) to be reflexive, it must satisfy the condition that \( m \) (the total number of ordered pairs in \( R \)) must be at least \( n \) (the number of elements in \( A \)). Thus, we can express this condition mathematically as:
\[ m \geq n \]

5. **Conclusion**:
Therefore, for a relation \( R \) to be reflexive on a set \( A \) with \( n \) elements, the number of ordered pairs \( m \) in \( R \) must satisfy the condition \( m \geq n \).

### Final Answer:
The condition is \( m \geq n \).

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