Association rules are binary partitions of an itemset? What does it mean?

Question

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?

Answer 1

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.