Let `A={1,\ 2,\ 3}` . Then, show that the number of relations containing (1, 2) and (2, 3) which are reflexive and transitive but not symmetric is three.

Explanation

To solve the problem, we need to find the number of relations on the set \( A = \{1, 2, 3\} \) that meet the following criteria:

1. The relations must contain the pairs \( (1, 2) \) and \( (2, 3) \).
2. The relations must be reflexive.
3. The relations must be transitive.
4. The relations must not be symmetric.

### Step 1: Identify Reflexive Pairs
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