Implicant

In Boolean logic, the term implicant has either a generic or a particular meaning. In the generic use, it refers to the hypothesis of an implication (implicant). In the particular use, a product term (i.e., a conjunction of literals) P is an implicant of a Boolean function F, denoted ${\displaystyle P\leq F}$, if P implies F (i.e., whenever P takes the value 1 so does F). For instance, implicants of the function

${\displaystyle f(x,y,z,w)=xy+yz+w}$

include the terms ${\displaystyle xy}$, ${\displaystyle xyz}$, ${\displaystyle xyzw}$, ${\displaystyle w}$, as well as some others.