(A and B) U (A - C) = A -(C - B)
$\displaystyle \left[\bigcup_{i=1}^{n} U_i \right]^c=\bigcap_{i=1}^{n}U_i^c$ where $\displaystyle ^c$ denotes the complement. An obvious corrolary of this is that $\displaystyle \left[\bigcap_{i=1}^{n}U_i\right]^c=\left[\bigcap_{i=1}^{n}\left(U_i^c\right)^c\right]^c=\left[\left[\bigcup_{i=1}^{n}U_i^c\right]^c\right]^c=\bigcup_{i=1}^{n}U_i^c$.