Proposition 6.3.6.1.2 (00PW): Properties of Unions of Families of Relations

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Let $A$ and $B$ be sets and let $\webleft\{ R_{i}\webright\} _{i\in I}$ be a family of relations from $A$ to $B$.

Interaction With Inverses. We have
\[ \webleft (\bigcup _{i\in I}R_{i}\webright )^{\dagger } = \bigcup _{i\in I}R^{\dagger }_{i}. \]

Proof of Proposition 6.3.6.1.2.

Item 1: Interaction With Inverses

Clear.

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