De Morgan's Laws (Set Theory)/Relative Complement/Complement of Union

Theorem
Let $S, T_1, T_2$ be sets such that $T_1, T_2$ are both subsets of $S$.

Then, using the notation of the relative complement:
 * $\relcomp S {T_1 \cup T_2} = \relcomp S {T_1} \cap \relcomp S {T_2}$

Proof
Let $T_1, T_2 \subseteq S$.

Then from Union is Smallest Superset:


 * $T_1 \cup T_2 \subseteq S$

Hence: