Access Database Design and Programming, Second Edition

Appendix B. The Quotient: An Additional Operation of the Relational Algebra

The quotient of two tables is not used often, but has a very specific use. It arises when we wish to select those rows of a table that are sufficient to provide all possible values in certain columns. As an example, imagine a business that makes furniture. The database for this business has a table on the types of wood that they use and on suppliers of wood and which types they supply. Examples are shown in Table 2.1 and Table 2.2 (of course, these tables would include more columns, but this is just to illustrate the point):

Table B-1. WOOD

Type
Mahogany
Red oak
Poplar
Walnut

Table B-2. SUPPLIER/TYPE

Sname	Type
Jones Wood Supply	mahogany
Austin Hardwoods	red oak
Orange Coast	mahogany
Jones Wood Supply	poplar
West Lumber	poplar
Jones Wood Supply	walnut
Austin Hardwoods	walnut
Jones Wood Supply	red oak
Orange Coast	walnut
West Lumber	red oak
Orange Coast	poplar
Orange Coast	red oak
Fred’s Woods	walnut

Note that there are four types of wood. Suppose we want to know which suppliers supply all four types—a reasonable question. The answer, which is shown in Table 2.3, is called the quotient.

Table B-3.  SUPPLIER/TYPE WOOD

Sname
Jones Wood Supply
Orange Coast

and is called the quotient of the table SUPPLIERS/TYPE by WOOD, written SUPPLIER/TYPE ÷ WOOD.

As you can see, the quotient can certainly come up in real-life situations. The reason for defining a specific operation for this ...