Association rules are binary partitions of an itemset? What does it mean? Let $$\\{Bread, Milk\\}, \\{Bread, Diaper, Beer, Eggs\\}, \\{ Milk, Diaper, Beer, Coke \\}, \\{Bread, Milk, Diaper, Beer \\}, \\{ Bread, Milk, Diaper, Coke \\}$$ be itemsets. Consider association rules such as: $$\\{Milk, Diaper\\} \rightarrow \\{ Beer \\}$$ $$\\{ Milk, Beer \\} \rightarrow \\{Diaper\\}$$ $$...$$ Then all "such" rules are _binary partitions_ of the itemset $\\{ Milk, Diaper, Beer\\}$. What does this mean?

The item-set $\\{ Milk, Diaper, Beer\\}$ has been partitioned into two nonempty parts, whose union is the whole itemset, one one the left-hand side and one on the right-hand side.