In
Boolean logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denote ...
, a product term is a conjunction of literals, where each literal is
either a variable or its negation.
Examples
Examples of product terms include:
:
:
:
Origin
The terminology comes from the similarity of AND
to multiplication as in the ring structure of
Boolean ring In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2.
Every Boolean ring gives rise to a Boolean al ...
s.
Minterms
For a
boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ( ...
of
variables
, a product term in which each of the
variables appears once (in either its complemented or uncomplemented form) is called a ''minterm''. Thus, a ''minterm'' is a logical expression of ''n'' variables that employs only the ''complement'' operator and the ''conjunction'' operator.
References
*Fredrick J. Hill, and Gerald R. Peterson, 1974, ''Introduction to Switching Theory and Logical Design, Second Edition'', John Wiley & Sons, NY, {{isbn, 0-471-39882-9
Boolean algebra