if A relation R in a set A is called ………… if `(a _(1), a _(2)) in R` implies `(a _(2) , a _(1)) in R` for all `a _(1) , a _(2) in A.`

Options

A. reflective
B. symmetric
C. transitive
D. equivalence

Answer

To solve the question, we need to define the type of relation described in the statement. The statement indicates that if a pair \((a_1, a_2)\) is in relation \(R\), then the pair \((a_2, a_1)\) must also be in relation \(R\) for all \(a_1, a_2\) in set \(A\). This definition corresponds to a specific type of relation in mathematics.

### Step-by-Step Solution:

1. **Understanding the Definition**:
- A relation \(R\) is defined on a set \(A\). The relation consists of ordered pairs of elements from the set \(A\).

2. **Analyzing the Given Condition**:
- The condition states that if \((a_1, a_2) \in R\), then it must also be true that \((a_2, a_1) \in R\). This means that the relation is bidirectional.

3. **Identifying the Type of Relation**:
- The property described is characteristic of a **symmetric relation**. In symmetric relations, the presence of one ordered pair implies the presence of its reverse.

4. **Conclusion**:
- Therefore, the relation \(R\) in set \(A\) is called a **symmetric relation**.

### Final Answer:
The relation \(R\) in set \(A\) is called a **symmetric relation**.