Set Difference with Union/Venn Diagram

Proof
Demonstration by Venn diagram:
 * Set-diff-with-union-1.png Set-diff-with-union-2.png Set-diff-with-union-3.png

Consider the diagram on the.

The red area forms $R \setminus \paren {S \cup T}$.

Consider the diagram in the middle.

The red and orange areas together form $R \setminus S$.

The red area alone forms $\paren {R \setminus S} \setminus T$.

Consider the diagram on the.

The red and orange areas together form $R \setminus T$.

The red area alone forms $\paren {R \setminus T} \setminus S$.

It is seen that the red areas are the same on all diagrams.