Show that the relation R in the set `{1, 2, 3}`given by `R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}`is reflexive but neither symmetric nor transitive.

Explanation

To show that the relation \( R \) in the set \( \{1, 2, 3\} \) given by \( R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)\} \) is reflexive but neither symmetric nor transitive, we will check each property step by step.

### Step 1: Check for Reflexivity
A relation \( R \) is reflexive if every element \( a \) in the set has the pair \( (a, a) \) in the relation.

- The set is \( \{1, 2, 3\} \).
- We need to check if \( (1, 1) \), \( (2, 2) \), and \( (3, 3) \) are in \( R \).
- From \( R \), we see:
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