Let $A,B$ be two sets. The following laws hold for the set intersection "$\cap$", set union "$\cup$" and set complent "$^C$":
$$\begin{array}{rcl}(A\cap B)^C&=&(A^C)\cup (B^C),\\(A\cup B)^C&=&(A^C)\cap (B^C).\end{array}$$
This law is named after Augustus De Morgan (1806 - 1871).
Proofs: 1
Proofs: 1