Thomas A. Alspaugh
Properties of Operations

Under Construction

Property Definition for operations ● and ○ As said in words
idempotent X●X = X ● is idempotent
commutative X●Y = Y●X ● is commutative
associative (X●Y)●Z = X●(Y●Z) ● is associative
distributive X●(Y○Z) = (X●Y)○(X●Z) ● distributes over ○
absorptive X●(X○Y) = X = X○(X●Y) ● and ○ are mutually absorbtive

Compare these with the reflexive, symmetric, and transitive properties of relations.

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