Show that the number of equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

Explanation

To solve the problem of finding the number of equivalence relations on the set {1, 2, 3} that contain the pairs (1, 2) and (2, 1), we will follow these steps:

### Step 1: Understand the properties of equivalence relations
An equivalence relation must satisfy three properties:
1. **Reflexivity**: For every element a in the set, (a, a) must be in the relation.
2. **Symmetry**: If (a, b) is in the relation, then (b, a) must also be in the relation.
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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