What is "implicant"

n. 1 (''propositional calculus'') The hypothesis of an implication 2 (context electrical engineering English) On a Karnaugh map: a set of 1's (whose quantity is a power of two) which are related by adjacency (i.e., the set is (w Connectivity (graph theory) connected), if the Karnaugh map is considered to be a graph which "wraps around" its edges, like a torus; and, all elements of the subgraph induced by the set have the same degree). ''Equivalently (in terms of Boolean algebra)'', a product term which, when true, always implies that the given Boolean function is true.

In Boolean logic, an implicant is a "covering" (sum term or product term) of one or more minterms in a sum of products (or maxterms in a product of sums) of a Boolean function. Formally, a product term P in a sum of products is an implicant of the Boolean function F if P implies F. More precisely:

P implies F (and thus is an implicant of F) if F also takes the value 1 whenever P equals 1.

where

• F is a Boolean function of n variables.
• P is a product term.

This means that P  ⇒  F with respect to the natural ordering of the Boolean space. For instance, the function

f(x, y, z, w) = xy + yz + w

is implied by xy, by xyz, by xyzw, by w and many others; these are the implicants of f.