Let R be a reflexive relation on a set A and I be the identity relation on A. Then

Options

A. `R sub I`
B. `I sub R`
C. `R = I`
D. none of these

Answer

To solve the problem, we need to analyze the properties of reflexive relations and the identity relation on a set A.

### Step-by-Step Solution:

1. **Understanding the Set A**:
Let’s define a set A. For example, let A = {1, 2, 3}.

**Hint**: Identify the elements of the set A clearly.

2. **Defining the Identity Relation I**:
The identity relation I on set A consists of pairs where each element is related to itself. Thus, for A = {1, 2, 3}, the identity relation I is:
\[ I = \{(1, 1), (2, 2), (3, 3)\} \]

**Hint**: Remember that the identity relation only includes pairs of the form (x, x) for each x in A.

3. **Defining a Reflexive Relation R**:
A reflexive relation R on set A must include all pairs (x, x) for every x in A. Therefore, R must also contain at least:
\[ R = \{(1, 1), (2, 2), (3, 3)\} \]
However, R can also include additional pairs, such as (1, 2), (2, 3), etc., as long as it maintains the reflexive property.

**Hint**: A reflexive relation must include all pairs of the form (x, x) for each element x in the set.

4. **Comparing R and I**:
Since R is a reflexive relation, it must contain at least the pairs that are in the identity relation I. Therefore, we can conclude that:
\[ I \subseteq R \]
However, R can also have additional pairs that are not in I.

**Hint**: Consider that while R must include I, it can also contain more elements.

5. **Determining the Relationship**:
The question asks whether R is a subset of I, I is a subset of R, R equals I, or none of these. Since R can contain additional pairs beyond those in I, we cannot say R equals I. However, we can say that I is a subset of R.

**Hint**: Analyze the definitions to see if one relation can be contained within the other.

6. **Conclusion**:
The correct conclusion is that:
\[ I \subseteq R \]
Thus, the answer is that I is a subset of R.

### Final Answer:
I is a subset of R.