Union Distributes over Intersection/Venn Diagram

Proof
Demonstration by Venn diagram:
 * UnionDistOverInt1.png UnionDistOverInt2.png

In the left hand diagram, $R$ is depicted in blue and $S \cap T$ is depicted in yellow.

Their intersection, where they overlap, is depicted in green.

Their union $R \cup \paren {S \cap T}$ is the total shaded area: yellow, blue and green.

In the right hand diagram, $\paren {R \cup S}$ is depicted in yellow and $\paren {R \cup T}$ is depicted in blue.

Their intersection, where they overlap, is depicted in green.

As can be seen by inspection, the areas are the same.