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Product term

## Summary

In Boolean logic, a product term is a conjunction of literals, where each literal is either a variable or its negation.

## Examples

Examples of product terms include:

${\displaystyle A\wedge B}$
${\displaystyle A\wedge (\neg B)\wedge (\neg C)}$
${\displaystyle \neg A}$

## Origin

The terminology comes from the similarity of AND to multiplication as in the ring structure of Boolean rings.

## Minterms

For a boolean function of ${\displaystyle n}$  variables ${\displaystyle {x_{1},\dots ,x_{n}}}$ , a product term in which each of the ${\displaystyle n}$  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