If R and R' are symmetric relations (not disjoint ) on a set A, then the relation `Rnn R'` is :

Options

A. reflexive
B. symmetric
C. transitive
D. None of these

Answer

To solve the problem, we need to determine the nature of the relation \( R \cap R' \) (the intersection of relations \( R \) and \( R' \)) given that both \( R \) and \( R' \) are symmetric relations on a set \( A \) and are not disjoint.

### Step-by-step Solution:

1. **Understanding Symmetric Relations**:
A relation \( R \) on a set \( A \) is symmetric if for every pair \( (a, b) \) in \( R \), the pair \( (b, a) \) is also in \( R \). Similarly, \( R' \) is symmetric.

2. **Assuming Elements in the Intersection**:
Let's assume there are elements \( a \) and \( b \) such that \( (a, b) \) is in \( R \cap R' \). This means that \( (a, b) \) is in both \( R \) and \( R' \).

3. **Using the Definition of Symmetry**:
Since \( (a, b) \) is in \( R \) and \( R \) is symmetric, it follows that \( (b, a) \) must also be in \( R \). Similarly, since \( (a, b) \) is in \( R' \) and \( R' \) is symmetric, \( (b, a) \) must also be in \( R' \).

4. **Conclusion about the Intersection**:
Therefore, \( (b, a) \) is in both \( R \) and \( R' \). This implies that \( (b, a) \) is in \( R \cap R' \).

5. **Final Result**:
Since for every pair \( (a, b) \) in \( R \cap R' \), the pair \( (b, a) \) is also in \( R \cap R' \), we conclude that \( R \cap R' \) is symmetric.

### Answer:
The relation \( R \cap R' \) is symmetric.