Characteristic of Cayley Table of Left Operation

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Let $S$ be a finite set.

Let $\leftarrow$ denote the left operation on $S$.

The Cayley table of the algebraic structure $\struct {S, \leftarrow}$ is characterised by the fact that each row contains just one distinct element.


A row of a Cayley table headed by $x$ contains all those elements of the form $x \leftarrow y$.

By definition of the left operation:

$x \leftarrow y = x$

Hence the result.


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