Suppose S is a set, and P={S} is a partition of S. Find the equivalence relation R corresponding to P.

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S be a set.

P= $\{S\}$ is a partition on S.

The equivalence relation R corresponding to P on S is following

For each a $\in S$ we denote the equivalence class of a as [a], which can be defined as,

[a]= $\{x\in S| xRa\}$ =S. This is the only equivalence class.

(Here R is defined on S, $xRa$ $\Leftrightarrow x,a\in S)$