A subalgebra of a power set algebra is called a field of sets; equivalently a field of sets is a set of subsets of some set " W " including the empty set and " W " and closed under finite union and complement with respect to " W " ( and hence also under finite intersection ).
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These are examples of an extremely important and powerful property of set algebra, namely, the "'principle of duality "'for sets, which asserts that for any true statement about sets, the "'dual "'statement obtained by interchanging unions and intersections, interchanging "'U "'and ?and reversing inclusions is also true.
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