Write the smallest reflexive relation on set `A={1,\ 2,\ 3,\ 4}` .

Explanation

To find the smallest reflexive relation on the set \( A = \{1, 2, 3, 4\} \), we need to understand what a reflexive relation is.

### Step-by-Step Solution:

1. **Definition of 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 included in the relation.

2. **Identify the Elements of Set \( A \)**: The set \( A \) contains the elements \( 1, 2, 3, \) and \( 4 \).

3. **Construct the Reflexive Relation**:
- For the element \( 1 \), we include the pair \( (1, 1) \).
- For the element \( 2 \), we include the pair \( (2, 2) \).
- For the element \( 3 \), we include the pair \( (3, 3) \).
- For the element \( 4 \), we include the pair \( (4, 4) \).

4. **Write the Smallest Reflexive Relation**: The smallest reflexive relation on the set \( A \) is:
\[ R = \{(1, 1), (2, 2), (3, 3), (4, 4)\} \]

### Final Answer:
The smallest reflexive relation on the set \( A = \{1, 2, 3, 4\} \) is:
\[ R = \{(1, 1), (2, 2), (3, 3), (4, 4)\} \]