The logical simplicity of boolean algebra enables the construction
of powerful, efficient search queries. The concept of boolean algebra is embedded
in human psychology, in our very biological understanding of how the world
works. It is the foundation for all of
mathematics,
most of science, and much of philosophy.
But more importantly, it is useful for the construction of advanced Internet search queries, and is used throughout the examples in the following pages.
The subsections below provide information on boolean
expressions, the boolean operators AND, OR,
and NOT, some boolean tricks,
and and a list of boolean capable search sites.
Expressions. It is easier to understand
boolean algebra when we compare it to the familiar arithmetic algebra we
learned in school, with the operators +, , x, / combined with operands
in expressions like the following:
( a + b ) x c
When we know the values of the operands of an algebraic expression, then
we can figure out the overall value. For example, if a=2, b =3, and c=4,
then the overall value of the above expression is 20.
Boolean algebra is very similar, with the logical operators AND, OR, and
NOT, combined with operands that can have either a value of True or False
in expressions like the following:
( a AND b ) OR c
Like any algebra, if you know the rules and value of the operands, you can
figure out the overall expression. In this case, if a=True, b=False, and
c=True, then the overall value of the above expression is True, according
to the rules described below.
AND. The most useful boolean operator is AND
because it combines truth values. An expression "a AND b" is True only
if both of the operands are True. For example, if a="You are wearing
glasses" and b="You are wearing a watch", then the overall expression is
true only if you are wearing both items of clothing at the same time, and
false if you are wearing only one item or neither. The rules of the AND
operator are shown in the truth table below.
a AND b

b 
False 
True 
a

False 
False 
False 
True 
False 
True 
AND Truth
Table
Or. The expression "A or B" is true if either of
the operands is true. For example, the expression "you are wearing a watch or you
are wearing glasses" is true if you are wearing either item or both, and
false only if you aren't wearing either. The truth table is shown below.
a OR b

b 
False 
True 
a 
False 
False 
True 
True 
True 
True 
OR
Truth Table
NOT. The NOT operator simply reverses the truth
of whatever it operates on. For example, the expression "I am not wearing
a watch" is True if you aren't wearing a watch, and False if you are. The
truth table is shown below.
a

NOT
a 
False 
True 
True 
False 
NOT
Truth Table
Tricks. Some of the most useful boolean algebra
tricks are listed below. Both sides of each listed expression are logically
equivalent, but the righthand side is in a shorter form. You can sometimes
use these tricks to reorder a long search query into a more manageable
form.
Long
Form

Shorter
Form

(
a AND b ) OR ( a AND c )

= a
AND ( b OR c ) 
(
a OR b ) AND ( a OR c )

= a
OR ( b AND c ) 
NOT
NOT a

= a 
NOT
a AND NOT b

= NOT
( a OR b ) 
NOT
a OR NOT b

= NOT
( a AND b ) 
Boolean sites. Boolean algebra queries
are supported by most search engines, but sometimes only through the "advanced" version.
Remember that the most common setting is to require boolean operators in
all CAPS or they won't be recognized, and that the NOT operator must often
be written as a minus sign, as in the following Google search query:
garden
AND (lettuce OR tomatoes) AND carrots
The following site search pages provide boolean search capability: