Question

A relation \(R\) on \[ A=\{1,2,3\} \] is defined as \[ R=\{(1,1),(3,3),(1,2)\}. \] Is \(R\) a symmetric relation? Justify your answer.

Write the smallest relation set \(R_1\) such that \[ R\cup R_1 \] becomes an equivalence relation on the set \[ \{1,2,3\}. \]

Hint:

To build an equivalence relation from a minimal set, sequentially satisfy reflexivity first, then symmetry, and lastly check transitivity to find the minimal required elements.

Answer 1