Set Difference is Right Distributive over Set Intersection/Venn Diagram

Proof
Demonstration by Venn diagram:
 * Set-diff-right-dist-intersection-1.png Set-diff-right-dist-intersection-2.png

Consider the diagram on the.

The red and yellow areas together form $A \cap B$.

The red area without the yellow area forms $\paren {A \cap B} \setminus C$.

Consider the diagram on the.

The red and orange areas together form $A \setminus C$.

The yellow and orange areas together form $B \setminus C$.

Their intersection is the orange area, which forms $\paren {A \setminus C} \cap \paren {B \setminus C}$.

It is seen that the red area on the is the same as the orange area on the.