Let `A = {1, 2, 3}`. Then number of equivalence relations containing (1, 2) is (A) 1 (B) 2 (C) 3 (D) 4

Explanation

To solve the problem of finding the number of equivalence relations on the set \( A = \{1, 2, 3\} \) that contain the pair \( (1, 2) \), we need to consider the properties of equivalence relations: reflexivity, symmetry, and transitivity.

### Step-by-Step Solution:

1. **Understanding Equivalence Relations**:
- An equivalence relation on a set must satisfy three properties:
- **Reflexive**: Every element is related to itself. For our set \( A \), this means \( (1, 1), (2, 2), (3, 3) \) must be included.
- **Symmetric**: If \( (a, b) \) is in the relation, then \( (b, a) \) must also be included. Since we have \( (1, 2) \), we must also include \( (2, 1) \).
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