# Contents

## Statement

###### Proposition

Let $f \colon X \longrightarrow Y$ be a function between sets. Let $\{S_i \subset Y\}_{i \in I}$ be a set of subsets of $Y$. Then

1. $f^{-1}\left( \underset{i \in I}{\cup} S_i\right) = \left(\underset{i \in I}{\cup} f^{-1}(S_i)\right)$ (the pre-image under $f$ of a union of subsets is the union of the pre-images)

2. $f^{-1}\left( \underset{i \in I}{\cap} S_i\right) \subset \left(\underset{i \in I}{\cap} f^{-1}(S_i)\right)$ (the pre-image under $f$ of the intersection of the subsets is the intersection of the pre-images).

For details see at interactions of images and pre-images with unions and intersections.

Last revised on May 20, 2017 at 13:15:24. See the history of this page for a list of all contributions to it.