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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 determine the properties of the relation \( R = \{(1, 2), (2, 1)\} \) in the set \( \{1, 2, 3\} \), we will check if it is symmetric, reflexive, and transitive. ### Step 1: Check for Symmetry A relation \( R \) is symmetric if for every pair \( (a, b) \in R \), the pair \( (b, a) \) is also in \( R \). - We have \( (1, 2) \in R \). The reverse pair \( (2, 1) \) is also in \( R \). - We have \( (2, 1) \in R \). The reverse pair \( (1, 2) \) is also in \( R \). ...
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