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. `m ge n`
B. `m le n`
C. `m=n`
D. none of these

Answer

To solve the problem, we need to analyze the properties of a reflexive relation on a finite set A with n elements.

### 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 for every element \( a \in A \), the pair \( (a, a) \) must be in the relation R.

2. **Identifying the Set A**:
Let’s denote the set A as \( A = \{a_1, a_2, a_3, ..., a_n\} \), where n is the number of elements in the set.

3. **Required Ordered Pairs for Reflexivity**:
For the relation R to be reflexive, it must contain the pairs \( (a_1, a_1), (a_2, a_2), ..., (a_n, a_n) \). Thus, there are exactly n pairs that must be present in R to satisfy the reflexive property.

4. **Total Ordered Pairs in R**:
The problem states that there are m ordered pairs in R. Since R is reflexive, we have established that at least n pairs must be included in R.

5. **Conclusion**:
Therefore, for R to be reflexive, the number of ordered pairs m must satisfy the condition:
\[ m \geq n \]
This means that the number of ordered pairs in the relation R must be at least equal to the number of elements in the set A.

### Final Answer:
Thus, we conclude that for a reflexive relation R on a finite set A having n elements, the number of ordered pairs m must satisfy:
\[ m \geq n \]