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The meet and join of partitions ? and ? are defined as follows. The meet is the partition whose blocks are the intersections of a block of ? and a block of ?, except for the empty set. In other words, a block of is the intersection of a block of ? and a block of ? that are not disjoint from each other. To define the join , form a relation on the blocks A of ? and the blocks B of ? by A ~ B if A and B are not disjoint. Then is the partition in which each block C is the union of a family of blocks connected by this relation.

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