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Combining and Negating Conditions with AND, OR, and NOT

You can specify multiple conditions in a single WHERE clause to, say, retrieve rows based on the values in multiple columns. You can use the AND and OR operators to combine two or more conditions into a compound condition. AND, OR, and a third operator, NOT, are logical operators. Logical operators, or Boolean operators, are operators designed to work with truth values: true, false, and unknown.

If you’ve programmed in other languages (or studied propositional logic), you’re familiar with the two-value logic (2VL) system. In two-value logic, the result of a logical expression is either true or false. 2VL assumes perfect knowledge, in which all propositions are known to be true or false. Databases model real data, however, and our knowledge of the world is imperfect—that’s why we use nulls to represent unknown values (see “Nulls” in Chapter 3).

2VL is insufficient to represent knowledge gaps, so SQL uses three-value logic (3VL). In three-value logic, the result of a logical expression is true, false, or unknown. If the result of a compound condition is false or unknown, the row is excluded from the result. (To retrieve rows with nulls, see “Testing for Nulls with IS NULL” later in this chapter.)

The AND operator

The AND operator’s important characteristics are:

  • AND connects two conditions and returns true only if both conditions are true.
  • Table 4.3 shows the possible outcomes when you combine two conditions with AND. The table’s left column shows the truth values of the first condition, the top row shows the truth values of the second condition, and each intersection shows the AND outcome. This type of table is called a truth table.

    Table 4.3.

    AND

    True

    False

    Unknown

    True

    True

    False

    Unknown

    False

    False

    False

    False

    Unknown

    Unknown

    False

    Unknown

  • Any number of conditions can be connected with ANDs. All the conditions must be true for the row to be included in the result.
  • AND is commutative (independent of order): WHERE condition1 AND condition2 is equivalent to WHERE condition2 AND condition1.
  • You can enclose one or both of the conditions in parentheses. Some compound conditions need parentheses to force the order in which conditions are evaluated.

See Listings 4.22 and 4.23, and Figures 4.22 and 4.23, for some AND examples.

Listing 4.22. List the biographies that sell for less than $20. See Figure 4.22 for the result.

SELECT title_name, type, price
  FROM titles
  WHERE type = 'biography' AND price < 20;

Figure 4.22 Result of Listing 4.22.

title_name                type       price
------------------------- ---------- -----
How About Never?          biography 19.95
Spontaneous, Not Annoying biography 12.99

Listing 4.23. List the authors whose last names begin with one of the letters H through Z and who don’t live in California. See Figure 4.23 for the result.

SELECT au_fname, au_lname
  FROM authors
  WHERE au_lname >= 'H'
    AND au_lname <= 'Zz'
    AND state <> 'CA';

Figure 4.23 Result of Listing 4.23. Remember that the results of string comparisons depend on the DBMS’s collating sequence; see “Sorting Rows with ORDER BY” earlier in this chapter.

au_fname  au_lname
--------- -----------
Wendy     Heydemark
Christian Kells
Paddy     O'Furniture

The OR operator

The OR operator’s important characteristics are:

  • OR connects two conditions and returns true if either condition is true or if both conditions are true.
  • Table 4.4 shows the OR truth table.

    Table 4.4.

    OR

    True

    False

    Unknown

    True

    True

    True

    True

    False

    True

    False

    Unknown

    Unknown

    True

    Unknown

    Unknown

  • Any number of conditions can be connected with ORs. OR will retrieve rows that match any condition or all the conditions.
  • Like AND, OR is commutative; the order in which you list the conditions doesn’t matter.
  • You can enclose one or both of the conditions in parentheses.

See Listings 4.24 and 4.25, and Figures 4.24 and 4.25, for some OR examples.

Listing 4.24. List the authors who live in New York State, Colorado, or San Francisco. See Figure 4.24 for the result.

SELECT au_fname, au_lname, city, state
  FROM authors
  WHERE (state = 'NY')
     OR (state = 'CO')
     OR (city = 'San Francisco');

Figure 4.24 Result of Listing 4.24.

au_fname  au_lname  city            state
--------- --------- --------------- -----
Sarah     Buchman   Bronx           NY
Wendy     Heydemark Boulder         CO
Hallie    Hull      San Francisco CA
Klee      Hull      San Francisco CA
Christian Kells     New York        NY

Listing 4.25. List the publishers that are located in California or are not located in California. This example is contrived to show the effect of nulls in conditions; see Figure 4.25 for the result.

SELECT pub_id, pub_name, state, country
  FROM publishers
  WHERE (state = 'CA')
    OR (state <> 'CA');

Figure 4.25 Result of Listing 4.25. Publisher P03 is missing because its state is null.

pub_id pub_name          state country
------ ----------------- ----- -------
P01    Abatis Publishers NY    USA
P02    Core Dump Books   CA    USA
P04    Tenterhooks Press CA    USA

Listing 4.25 shows the effect of nulls in conditions. You might expect the result, Figure 4.25, to display all the rows in the table publishers. But the row for publisher P03 (located in Germany) is missing because it contains a null in the column state. The null causes the result of both of the OR conditions to be unknown, so the row is excluded from the result. To test for nulls, see “Testing for Nulls with IS NULL” later in this chapter.

The NOT operator

The NOT operator’s important characteristics are:

  • Unlike AND and OR, NOT doesn’t connect two conditions. Instead, it negates (reverses) a single condition.
  • Table 4.5 shows the NOT truth table.

    Table 4.5.

    CONDITION

    NOT CONDITION

    True

    False

    False

    True

    Unknown

    Unknown

  • In comparisons, place NOT before the column name or expression

    WHERE NOT state = 'CA'     --Correct

    and not before the operator (even though it sounds better when read):

    WHERE state NOT = 'CA'     --Illegal
  • NOT acts on one condition. To negate two or more conditions, repeat the NOT for each condition. To list titles that are not biographies and are not priced less than $20, for example, type

    SELECT title_id, type, price
      FROM titles
      WHERE NOT type = 'biography'
        AND NOT price < 20;    --Correct

    and not

    SELECT title_id, type, price
      FROM titles
      WHERE NOT type = 'biography'
        AND price < 20;         --Wrong

    The latter clause is legal but returns the wrong result. See the Tips in this section to learn ways to express equivalent NOT conditions.

  • In comparisons, using NOT often is a matter of style. The following two clauses are equivalent:

    WHERE NOT state = 'CA'

    and

    WHERE state <> 'CA'
  • You can enclose the condition in parentheses.

Listing 4.26. List the authors who don’t live in California. See Figure 4.26 for the result.

SELECT au_fname, au_lname, state
  FROM authors
  WHERE NOT (state = 'CA');

Figure 4.26 Result of Listing 4.26.

au_fname  au_lname    state
--------- ----------- -----
Sarah     Buchman     NY
Wendy     Heydemark   CO
Christian Kells       NY
Paddy     O'Furniture FL

Listing 4.27. List the titles whose price is not less than $20 and that have sold more than 15,000 copies. See Figure 4.27 for the result.

SELECT title_name, sales, price
  FROM titles
  WHERE NOT (price < 20)
    AND (sales > 15000);

Figure 4.27 Result of Listing 4.27.

title_name                    sales   price
----------------------------- ------- -----
Ask Your System Administrator   25667 39.95
I Blame My Mother             1500200 23.95

Using AND, OR, and NOT together

You can combine the three logical operators in a compound condition. Your DBMS uses SQL’s precedence rules to determine which operators to evaluate first. Precedence is covered in “Determining the Order of Evaluation” in Chapter 5, but for now you need know only that when you use multiple logical operators in a compound condition, NOT is evaluated first, then AND, and finally OR. You can override this order with parentheses: Everything in parentheses is evaluated first. When parenthesized conditions are nested, the innermost condition is evaluated first. Under the default precedence rules, the condition x AND NOT y OR z is equivalent to (x AND (NOT y)) OR z. It’s wise to use parentheses, rather than rely on the default evaluation order, to make the evaluation order clear.

If I want to list history and biography titles priced less than $20, for example, Listing 4.28 won’t work. AND is evaluated before OR, so the query is evaluated as follows:

  1. Find all the biography titles less than $20.
  2. Find all the history titles (regardless of price).
  3. List both sets of titles in the result (Figure 4.28).

Listing 4.28. This query won’t work if I want to list history and biography titles less than $20, because AND has higher precedence than OR. See Figure 4.28 for the result.

SELECT title_id, type, price
  FROM titles
  WHERE  type  = 'history'
     OR  type  = 'biography'
     AND price < 20;

Figure 4.28 Result of Listing 4.28. This result contains two history titles priced more than $20, which is not what I wanted.

title_id type      price
-------- --------- -----
T01      history  21.99
T02      history   19.95
T06      biography 19.95
T12      biography 12.99
T13      history  29.99

To fix this query, I’ll add parentheses to force evaluation of OR first. Listing 4.29 is evaluated as follows:

  1. Find all the biography and history titles.
  2. Of the titles found in step 1, keep the ones priced less than $20.
  3. List the subset of titles in the result (Figure 4.29).

Listing 4.29. To fix Listing 4.28, I’ve added parentheses to force OR to be evaluated before AND. See Figure 4.29 for the result.

SELECT title_id, type, price
  FROM titles
  WHERE  (type  = 'history'
     OR  type  = 'biography')
     AND price < 20;

Figure 4.29 Result of Listing 4.29. Fixed.

title_id type      price
-------- --------- -----
T02      history   19.95
T06      biography 19.95
T12      biography 12.99
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