A logical conjunction of literals is an implicant of a Boolean function if every Boolean valuation making true also makes true. Every term in a disjunctive normal form is an implicant of the represented Boolean function. To rule out a one-literal term, it suffices to find a false Boolean valuation of where that literal is true.
An implicant from which no literal can be removed while preserving the implication to the Boolean function. A prime implicant is essential when it covers a one-input assignment that no other prime implicant covers.
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In the context of Boolean algebra and digital logic design, an **implicant** is a combination of input variables that results in the output of a Boolean function being true (or "1"). More specifically, an implicant is defined as a product term (a conjunction of literals) in a Boolean expression that covers one or more minterms (combinations of variable states that yield a true output).