Chapter 7 - Thinking in Sets

In this chapter, you will learn What Is a Set, Anyway,Operations on Sets, Intersection, Difference, Union and SQL Set Operations.

Difference

What's the difference between 21 and 10? If you answered 11, you're on the right track! A difference operation (sometimes also called subtract, minus, or except) takes one set of values and removes the set of values from a second set. What remains is the set of values in the first set that are not in the second set. (As you'll see later, EXCEPT is the keyword used in the SQL Standard.)

Difference in Set Theory

Difference is another very powerful mathematical tool. As a scientist, you might be interested in finding what's different about two sets of chemical or physical sample data. For example, a pharmaceutical research chemist might have two compounds that seem to be very similar, but one provides a certain beneficial effect and the other does not. Finding what's different about the two compounds might help uncover why one works and the other does not. As an engineer,you might have two similar designs,but one works better than the other. Finding the difference between the two designs could be crucial to eliminating structural flaws in future buildings.

Let's take a look at difference in action by examining two sets of numbers.

The first set of numbers is as follows.

1, 5, 8, 9, 32, 55, 78

The second set of numbers is as follows.

3, 7, 8, 22, 55, 71, 99

The difference of the first set of numbers minus the second set of numbers is the numbers that exist in the first set but not the second.

1, 5, 9, 32, 78

Note that you can turn the previous difference operation around. Thus, the difference of the second set minus the first set is

3, 7, 22, 71, 99

The members of each set don't have to be single values. In fact, you'll most likely be dealing with sets of rows when trying to solve problems with SQL. Earlier in this chapter we said that when a member of a set is something more than a single number or value, each member of the set has multiple attributes (bits of information that describe the properties of each member). For example, your favorite stew recipe is a complex member of the set of all recipes that contains many different ingredients. You can think of each ingredient as an attribute of your complex stew member.

To find the difference between two sets of complex set members,you have to find the members that match on all the attributes in the second set with members in the first set. Don't forget that all of the members in each set you're trying to compare must have the same number and type of attributes. Remove from the first set all the matching members you find in the second set,and the result is the difference. For example, suppose you have a complex set like the one below. Each row represents a member of the set (a stew recipe),and each column denotes a particular attribute (an ingredient).

Potatoes	Water	Lamb	Peas
Rice	Chicken Stock	Chicken	Carrots
Pasta	Water	Tofu	Snap Peas
Potatoes	Beef Stock	Beef	Cabbage
Pasta	Water	Pork	Onions

A second set might look like this.

Potatoes	Water	Lamb	Onions
Rice	Chicken Stock	Turkey	Carrots
Pasta	Vegetable Stock	Tofu	Snap Peas
Potatoes	Beef Stock	Beef	Cabbage
Beans	Water	Pork	Onions

The difference of the first set minus the second set is the objects in the first set that don't exist in the second set.

Potatoes	Water	Lamb	Peas
Rice	Chicken Stock	Chicken	Carrots
Pasta	Water	Tofu	Snap Peas
Pasta	Water	Pork	Onions

Difference between Result Sets

When you're dealing with rows in a set of data fetched with SQL, the attributes are the individual columns. For example, suppose you have a set of rows returned by a query like the following one. (These are recipes from John's cookbook.)

Recipe	Starch	Stock	Meat	Vegetable
Lamb Stew	Potatoes	Water	Lamb	Peas
Chicken Stew	Rice	Chicken Stock	Chicken	Carrots
Veggie Stew	Pasta	Water	Tofu	Snap Peas
Irish Stew	Potatoes	Beef Stock	Beef	Cabbage
Pork Stew	Pasta	Water	Pork	Onions

A second query result set might look like the following. (These are recipes from Mike's cookbook.)

Recipe	Starch	Stock	Meat	Vegetable
Lamb Stew	Potatoes	Water	Lamb	Peas
Turkey Stew	Rice	Chicken Stock	Turkey	Carrots
Veggie Stew	Pasta	Vegetable Stock	Tofu	Snap Peas
Irish Stew	Potatoes	Beef Stock	Beef	Cabbage
Pork Stew	Beans	Water	Pork	Onions

The difference between John's recipes and Mike's recipes (John's minusMike's) is all the recipes in John's cookbook that do not appear in Mike's cookbook.

Recipe	Starch	Stock	Meat	Vegetable
Lamb Stew	Potatoes	Water	Lamb	Peas
Chicken Stew	Rice	Chicken Stock	Chicken	Carrots
Veggie Stew	Pasta	Water	Tofu	Snap Peas
Pork Stew	Pasta	Water	Pork	Onions

You can also turn this problem around. Suppose you want to find the recipes in Mike's cookbook that are not in John's cookbook. Here's the answer.

Recipe	Starch	Stock	Meat	Vegetable
Lamb Stew	Potatoes	Water	Lamb	Peas
Turkey Stew	Rice	Chicken Stock	Turkey	Carrots
Veggie Stew	Pasta	Vegetable Stock	Tofu	Snap Peas
Pork Stew	Beans	Water	Pork	Onions

Again,we can use a set diagram to help visualize how a difference operation works. Let's assume you have a nice database containing all your favorite recipes. You really do not like the way onions taste with beef,so you're interested in finding all recipes that contain beef but not onions. Figure 7-3 shows you the set diagram that helps you visualize how to solve this problem.



Figure 7-3 Finding out which recipes have beef but not onions

The upper full circle represents the set of recipes that contain beef. The lower full circle represents the set of recipes that contain onions. As you remember from the discussion about INTERSECT,where the two circles overlap is where you'll find the recipes that contain both. The dark-shaded part of the upper circle that's not part of the overlapping area represents the set of recipes that contain beef but do not contain onions. Likewise, the part of the lower circle that's not part of the overlapping area represents the set of recipes that contain onions but do not contain beef.

You probably know that you first ask SQL to fetch all the recipes that have beef. Next, you ask SQL to fetch all the recipes that have onions. (As you'll see later in this chapter, the special SQL keyword EXCEPT links the two queries to get the final answer.)

Are you falling into the trap again? (You did read Chapter 2, didn't you?) If your recipe table looks like the samples earlier, you might think that you could simply say the following.

"Show me the recipes that have beef as the meat ingredient and that do not have onions as the vegetable ingredient."

Translation	Select the recipe name from the recipes table where meat ingredient is beef and vegetable ingredient is not onions
Clean Up	Select the recipe name from the recipes table where meat ingredient is = beef and vegetable ingredient is not <> onions
SQL	SELECT RecipeName FROM Recipes WHERE MeatIngredient = 'Beef' AND VegetableIngredient <> 'Onions'

Again, as you learned in Chapter 2, a single Recipes table isn't such a hot idea. (Pun intended!) What about recipes that have ingredients other than meat and vegetables? What about the fact that some recipes have many ingredients and others have only a few? A correctly designed Recipes database will have a separate Recipe_Ingredients table with one row per recipe per ingredient. Each ingredient row will have only one ingredient, so no one row can be both beef and onions at the same time. You'll need to first find all the beef rows, then find all the onions rows, then difference them on RecipeID.

How about a more complex problem? Let's say you hate carrots, too. A set diagram to visualize the solution might look like Figure 7-4.

First you need to find the set of recipes that have beef, and then get the difference with either the set of recipes containing onions or the set containing



Figure 7-4 Finding out which recipes have beef but no onions or carrots

carrots. Take that result and get the difference again with the remaining set (onions or carrots) to leave only the recipes that have beef but no carrots or onions (the light-shaded area in the upper circle).

Problems You Can Solve with Difference

Unlike intersection (which looks for common members of two sets), difference looks for members that are in one set but not in another set. Here's just a small sample of the problems you can solve using a difference technique with data from the sample databases.

"Show me customers whose names are not the same as any employee."
"Find all the customers who ordered a bicycle but did not order a helmet."
"List the entertainers who played engagements for customer Bonnicksen but did not play any engagement for customer Rosales."
"Show me the students who have an average score of 85 or better in Art but do not have an average score of 85 or better in Computer Science."
"Find the bowlers who had a raw score of 155 or better at Thunderbird Lanes but not at Bolero Lanes."
"Show me the recipes that have beef but not garlic."

One of the limitations of using a pure difference is that the values must match in all the columns in each result set. This works well if you're finding the difference between two or more sets from the same table-for example, customers who ordered bicycles and customers who ordered helmets. It also works well when you're finding the difference between sets from tables that have similar columns-for example, customer names and employee names.

In many cases, however, you'll want to find solutions that require a match on only a few column values from each set. For this type of problem, SQL provides an OUTER JOIN operation, which is an intersection on key values that includes the unmatched values from one or both of the two sets. Here's a sample of problems you can solve with an OUTER JOIN.

"Show me customers who do not live in the same city as any employees." (OUTER JOIN on the city name.)
"List customers and the entertainers they did not book." (OUTER JOIN on the engagement number.)
"Find the agents who are not in the same ZIP Code as any entertainer." (OUTER JOIN on the ZIP Code.)
"Show me the students who do not have the same first name as any teachers." (OUTER JOIN on the first name.)
"Find the bowlers who have an average of 150 or higher who have never bowled a game below 125." (OUTER JOIN on the bowler ID from two different tables.)
"Display all the ingredients for recipes that do not have carrots."(OUTER JOIN on the recipe ID.)

Don't worry! We'll show you all about solving these problems (and more) using OUTER JOINs in Chapter 9. Also, because few commercial implementations of SQL support EXCEPT (the keyword for difference),we'll show how to use an OUTER JOIN to solve many problems that might otherwise require an EXCEPT.