# De Morgan's Laws (Set Theory)/Set Complement/Complement of Intersection/Venn Diagram

## Theorem

$\overline {T_1 \cap T_2} = \overline T_1 \cup \overline T_2$

## Proof

Demonstration by Venn diagram:

$\overline T_1$ is depicted in yellow and $\overline T_2$ is depicted in red.

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

Their union $\overline T_1 \cup \overline T_2$ is the total shaded area: yellow, red and orange.

As can be seen by inspection, this also equals the complement of the intersection of $T_1$ and $T_2$.