// Workers AI · dad joke modeWhat did the product term say? "I multiply the fun.

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:

$A\wedge B$

$A\wedge (\neg B)\wedge (\neg C)$

$\neg A$

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