Definition:Operation Compatible with Set Equivalence

Definition
Let $F$ be a (unary) operation which can be applied to sets.

Then $F$ is compatible with set equivalence :


 * $F \left({A}\right) = F \left({B}\right) \iff A \sim B$

where:
 * $A$ and $B$ are arbitrary sets
 * $\sim$ denotes set equivalence.