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

Explanation

To show that the number of equivalence relations in the set \(\{1, 2, 3\}\) containing the pairs \((1, 2)\) and \((2, 1)\) is two, we will follow these steps:

### Step 1: Understanding Equivalence Relations
An equivalence relation must satisfy three properties:
1. **Reflexive**: For every element \(a\), the pair \((a, a)\) must be in the relation.
2. **Symmetric**: If \((a, b)\) is in the relation, then \((b, a)\) must also be in the relation.
3. **Transitive**: If \((a, b)\) and \((b, c)\) are in the relation, then \((a, c)\) must also be in the relation.

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