# Set operations (SQL)

Set operations in SQL is a type of operations which allow the results of multiple queries to be combined into a single result set.[1]

Set operators in SQL include `UNION`, `INTERSECT`, and `EXCEPT`, which mathematically correspond to the concepts of union, intersection and set difference.

## UNION operator

In SQL the `UNION` clause combines the results of two SQL queries into a single table of all matching rows. The two queries must result in the same number of columns and compatible data types in order to unite. Any duplicate records are automatically removed unless `UNION ALL` is used.

`UNION` can be useful in data warehouse applications where tables are not perfectly normalized.[2] A simple example would be a database having tables `sales2005` and `sales2006` that have identical structures but are separated because of performance considerations. A `UNION` query could combine results from both tables.

Note that `UNION ALL` does not guarantee the order of rows. Rows from the second operand may appear before, after, or mixed with rows from the first operand. In situations where a specific order is desired, `ORDER BY` must be used.

Note that `UNION ALL` may be much faster than plain `UNION`.

### Examples

Given these two tables:

sales2005
person amount
Joe 1000
Alex 2000
Bob 5000
sales2006
person amount
Joe 2000
Alex 2000
Zach 35000

Executing this statement:

`SELECT * FROM sales2005 UNION SELECT * FROM sales2006; `

yields this result set, though the order of the rows can vary because no `ORDER BY` clause was supplied:

person amount
Joe 1000
Alex 2000
Bob 5000
Joe 2000
Zach 35000

Note that there are two rows for Joe because those rows are distinct across their columns. There is only one row for Alex because those rows are not distinct for both columns.

`UNION ALL` gives different results, because it will not eliminate duplicates. Executing this statement:

`SELECT * FROM sales2005 UNION ALL SELECT * FROM sales2006; `

would give these results, again allowing variance for the lack of an `ORDER BY` statement:

person amount
Joe 1000
Joe 2000
Alex 2000
Alex 2000
Bob 5000
Zach 35000

The discussion of full outer joins also has an example that uses `UNION`.

## INTERSECT operator

The SQL `INTERSECT` operator takes the results of two queries and returns only rows that appear in both result sets. For purposes of duplicate removal the `INTERSECT` operator does not distinguish between `NULLs`. The `INTERSECT` operator removes duplicate rows from the final result set. The `INTERSECT ALL` operator does not remove duplicate rows from the final result set, but if a row appears X times in the first query and Y times in the second, it will appear ${\displaystyle \min(X,Y)}$ times in the result set.

### Example

The following example `INTERSECT` query returns all rows from the Orders table where Quantity is between 50 and 100.

`SELECT * FROM   Orders WHERE  Quantity BETWEEN 1 AND 100  INTERSECT  SELECT * FROM   Orders WHERE  Quantity BETWEEN 50 AND 200; `

## EXCEPT operator

The SQL `EXCEPT` operator takes the distinct rows of one query and returns the rows that do not appear in a second result set. For purposes of row elimination and duplicate removal, the `EXCEPT` operator does not distinguish between `NULLs`. The `EXCEPT ALL` operator does not remove duplicates, but if a row appears X times in the first query and Y times in the second, it will appear ${\displaystyle \max(X-Y,0)}$ times in the result set.

Notably, the Oracle platform provides a `MINUS` operator which is functionally equivalent to the SQL standard `EXCEPT DISTINCT` operator.[3]

### Example

The following example `EXCEPT` query returns all rows from the Orders table where Quantity is between 1 and 49, and those with a Quantity between 76 and 100.

Worded another way; the query returns all rows where the Quantity is between 1 and 100, apart from rows where the quantity is between 50 and 75.

`SELECT * FROM   Orders WHERE  Quantity BETWEEN 1 AND 100  EXCEPT  SELECT * FROM   Orders WHERE  Quantity BETWEEN 50 AND 75; `

### Example

The following example is equivalent to the above example but without using the `EXCEPT` operator.

`SELECT o1.* FROM (     SELECT *     FROM Orders     WHERE Quantity BETWEEN 1 AND 100) o1 LEFT JOIN (     SELECT *     FROM Orders     WHERE Quantity BETWEEN 50 AND 75) o2 ON o1.id = o2.id WHERE o2.id IS NULL `

2. ^ "a `UNION ALL` views technique for managing maintenance and performance in your large data warehouse environment ... This `UNION ALL` technique has saved many of my clients with issues related to time-sensitive database designs. These databases usually have an extremely volatile current timeframe, month, or day portion and the older data is rarely updated. Using different container DASD allocations, tablespaces, tables, and index definitions, the settings can be tuned for the specific performance considerations for these different volatility levels and update frequency situations." Terabyte Data Warehouse Table Design Choices - Part 2 (accessed on July 25, 2006)
3. ^ "E071-03, `EXCEPT DISTINCT` table operator: Use `MINUS` instead of `EXCEPT DISTINCT`" "Oracle Compliance To Core SQL:2003". Docs.oracle.com. Retrieved 7 July 2022.