Greenwood press

SURFACE AREA
135

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Ultracapacitors

Unfolding the human brain

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SYMBOLIC LOGIC
The nineteenth-century mathematician George Boole is the acknowledged
founder of modern symbolic logic. He recognized that an algebra of logic could
be developed following the model of the algebra of real numbers. The variables
of the algebra are statements that have one of two values: TRUE (1) or FALSE
(0). The fundamental operations are NOT, AND, and OR, as opposed to the num-
ber operations of opposite, multiplication, and addition. The algebra of logic
underlies decision-making, modern electronics, library searches, and branching
in computer programs.
Computer software is built on logical structures. If a market analyst had to
select all of the California residents who were female from a computer database
of customers in the United States, the status of each person in the database would
be evaluated with an expression such as “this person is from California and this
person is a women.” Sarah Jones (female) from San Francisco would evaluate as
TRUE for both parts. Amy Redfox (female) from Arizona would be evaluated as
FALSE AND TRUE. Since Amy misses one criterion, she should be excluded
from the final set. Hence the value for Amy should be FALSE AND TRUE =
FALSE. Although there may be millions of people in the database, each one falls
into only one of four categories of logic. If you use a spreadsheet program, you
can build truth tables that show the relationships among NOT, AND, and OR for
these four cases. In the table below, all possible cases of statements p and q are
listed using the words TRUE and FALSE. Each case has been evaluated with the
spreadsheet’s functions for logic. For example, the spreadsheet formula in cell
D2 is = AND(A2,B2). The formula in cell E4 is = OR(A4,B4). The last column
gives truth values of an expression that uses of all of the Boolean operations.