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

• Right Operation is Anticommutative

Sources

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