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Show that the relation R in the set {1, ...

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

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To show that the relation \( R \) in the set \( \{1, 2, 3\} \) given by \( R = \{(1, 2), (2, 1)\} \) is symmetric but neither reflexive nor transitive, we will analyze the properties of the relation step by step. ### Step 1: Check if the relation is symmetric A relation \( R \) is symmetric if for every \( (a, b) \in R \), it also holds that \( (b, a) \in R \). - We have the pairs in \( R \): - \( (1, 2) \) - \( (2, 1) \) ...
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