Left Operation is Anticommutative

Theorem

The left operation is anticommutative:

$\forall x, y: x \leftarrow y = y \leftarrow x \iff x = y$


Proof

Immediate from the definition of the left operation.

$\blacksquare$


Also see


Sources

  • 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Exercise $2.17 \ \text{(a)}$
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