Frequent item sets are not very useful by themselves. The next step is to build association rules. Because of this final goal, the whole field of basket analysis is sometimes called association rule mining.
An association rule is a statement of the type, if X, then Y—for example, if a customer bought War and Peace, then they will buy Anna Karenina. Note that the rule is not deterministic (not all customers who buy X will buy Y), but it is rather cumbersome to always spell it out: if a customer bought X, they are more likely than baseline to buy Y; thus, we say if X, then Y, but we mean it in a probabilistic sense.
Interestingly, both the antecedent and the conclusion may contain multiple objects: customers who bought X, Y, and Z also bought A, B, and C. Multiple antecedents may allow you to make more specific predictions than are possible from a...