Exercise 4: Consider the following relational schema: Sale(clerk, store, city, date, item, size, color) I/ a clerk sold an item on a particular day Item(item, size, color, price) I/ prices and available sizes and colors for items Make the following assumptions, and only these assumptions, about the real world being modeled: - Each clerk works in one store. - Each store is in one city. - A given item always has the same price, regardless of size or color. - Each item is available in one or more sizes and one or more colors, and each item is available in all combinations of sizes and colors for that item. Sale does not contain duplicates: If a clerk sells more than one of a given item in a given size and color on a given day, still only one tuple appears in relation Sale to record that fact. (a) Specify a set of completely nontrivial functional dependencies for relations Sale and Item that encodes the assumptions described above and no additional assumptions. (b) Based on your functional dependencies in part (a), specify all minimal keys for relations Sale and Item. (c) Is the schema in Boyce-Codd Normal Form (BCNF) according to your answers, to (a) and (b)? If not, give a decomposition into BCNF