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While at most two sets are joined in any Boolean operation, the new set formed by that operation can then be joined with another set using a new Boolean operation. Using the previous example, we can define a new set C as the "set of all dehydrated objects". Then "set A AND set B AND set C" would be all degydrated red apples.
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Let's define symbols for the two binary operations as <math>\land / \cap</math> (logical AND/intersection) and <math>\lor / \cup</math> (logical OR/union), and a single unary operation <math>\lnot</math> / ~ (logical NOT/complement) and two elements, 0 (logical FALSE/the empty set) and 1 (logical TRUE/the universe), such that, for all sets ''a'', ''b'' and ''c'' the following rules apply:
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