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

Explanation

To determine the number of equivalence relations on the set \( A = \{1, 2, 3\} \) that contain the pair \( (1, 2) \), we will follow these steps:

### Step 1: Understand the properties of equivalence relations
An equivalence relation must satisfy three properties:
1. **Reflexivity**: Every element must be related to itself. Therefore, \( (1, 1) \), \( (2, 2) \), and \( (3, 3) \) must be included.
2. **Symmetry**: If \( (a, b) \) is in the relation, then \( (b, a) \) must also be in the relation. Since \( (1, 2) \) is included, \( (2, 1) \) must also be included.
3. **Transitivity**: If \( (a, b) \) and \( (b, c) \) are in the relation, then \( (a, c) \) must also be in the relation.

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