The price of each item in a store is nonnegative. The store manager is only interested in mining the rules, following the constraints given below. For each of the following cases, identify the kinds of constraints they represent and briefly discuss how to mine such association rules using constraint-based pattern mining.

a. Containing at least one Blu-ray DVD movie.

b. Containing items with a sum of the prices that is less than \(\$ 150\).

c. Containing one free item and other items with a sum of the prices that is at least \(\$ 200\), whereas the average price of all the items is between \(\$ 100\) and \(\$ 500\).