Consider the following six relations for an order-processing database application in a company:

CUSTOMER (Cust#, Cname, City)
ORDER (Order#, Odate, Cust#, Ord_Amt)
ORDER_ITEM (Order#, Item#, Qty)
ITEM (Item#, Unit_price)
SHIPMENT (Order#, Warehouse#, Ship_date)
WAREHOUSE (Warehouse#, City)

Here, Ord_Amt refers to total dollar amount of an order; Odate is the date the order was placed; Ship_date is the date an order (or part of an order) is shipped from the warehouse. Assume that an order can be shipped from several warehouses. Specify the foreign keys for this schema, stating any assumptions you make. What other constraints can you think of for this database?

Strictly speaking, a foreign key is a set of attributes, but when that set contains only one attribute, then that attribute itself is often informally called a foreign key. The schema of this question has the following five foreign keys:
1. the attribute Cust# of relation ORDER that references relation CUSTOMER,
2. the attribute Order# of relation ORDER_ITEM that references relation ORDER,
3. the attribute Item# of relation ORDER_ITEM that references relation ITEM,
4. the attribute Order# of relation SHIPMENT that references relation ORDER, and
5. the attribute Warehouse# of relation SHIPMENT that references relation WAREHOUSE.
We now give the queries in relational algebra:

The above query lists all orders for which no “timely” shipment was made, including orders for which no shipment was ever made. It is instructive to compare the above query with the one below that lists those orders for which at least one “late” shipment was made.