Sequence of fulfillment of UNION, EXCEPT, and INTERSECT operators

When solving exercise #6 (SELECT) of the rating stage we had to answer the question of precedence of UNION, EXCEPT, and INTERSECT operations.  Martin Gruber [4] in his “SQL Instant Reference” suggests the following logical sequence of their fulfillment:

• UNION, EXCEPT
• INTERSECT

If we presume that the logical sequence of fulfillment of operations corresponds to their precedence, than the precedence of UNION and EXCEPT operations is identical and, as a result, they should be fulfilled in accordance with the sequence in which they are recorded, and this sequence is not changed by placement of the brackets. Thereby both of the operations are fulfilled before INTERSECT operation, i.e. they have precedence over it.

Let’s analyze three simple queries, which we will combine in different ways in order to prove the aforementioned claims:

--Models and types of products of producer B  
  
SELECT model, type FROM Product WHERE maker='B';

--Laptop models  
  
SELECT model, type FROM Product WHERE type='Laptop';

--PC Model  
SELECT model, type FROM Product WHERE type='PC';

Let’s prove the first claim. If EXCEPT operation has precedence over UNION operation, then the queries

SELECT model, type FROM Product WHERE maker='B'  
UNION  
SELECT model, type FROM Product WHERE type='Laptop'  
EXCEPT  
SELECT model, type FROM Product WHERE type='PC';

(SELECT model, type FROM Product WHERE maker='B'  
UNION  
SELECT model, type FROM Product WHERE type='Laptop')  
EXCEPT  
SELECT model, type FROM Product WHERE type='PC';

Similarly, if UNION operation has precedence over EXCEPT operation, then the queries

SELECT model, type FROM Product WHERE type='Laptop'
EXCEPT  
SELECT model, type FROM Product WHERE type='PC'  
UNION  
SELECT model, type FROM Product WHERE maker='B';

(SELECT model, type FROM Product WHERE type='Laptop'  
EXCEPT  
SELECT model, type FROM Product WHERE type='PC')  
UNION  
SELECT model, type FROM Product WHERE maker='B';

Thus, UNION and EXCEPT operations are equivalent in terms of precedence.

Let’s check precedence of INTERSECT operation as compared to other statements (in test problems one can choose any of them, as both of them have the same sequence).

If INTERSECT is inferior in precedence or equivalent to UNION, then the queries

SELECT model, type FROM Product WHERE maker='B'  
UNION  
SELECT model, type FROM Product WHERE type='Laptop'  
INTERSECT  
SELECT model, type FROM Product WHERE type='PC';

(SELECT model, type FROM Product WHERE maker='B'  
UNION  
SELECT model, type FROM Product WHERE type='Laptop')  
INTERSECT  
SELECT model, type FROM Product WHERE type='PC';

Conclusion. Logical sequence, suggested in the beginning of the article, does not correspond to the order of precedence of the operations, and, to my mind, it should be reversed:

• INTERSECT
• UNION, EXCEPT