Inverse of Small Relation is Small

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Let $a$ be a small class.

Let $a$ also be a relation.

Then the inverse relation of $a$ is small.


Let $A$ equal:

$\set {\tuple {\tuple {x, y}, \tuple {y, x} } : \tuple {x, y} \in a}$

Then $A$ maps $a$ to its inverse.

Thus, the inverse of $a$ is the image of $a$ under $A$.

By Image of Small Class under Mapping is Small, the inverse of $a$ is small.