 Satisfying assignment

A satisfying assignment is a complete Boolean valuation $v$ for which a Boolean formula $F$ has truth value one, written $v\models F$. The notation describes a relation between the Boolean valuation and the Boolean formula. For the example in Boolean satisfiability problem, $(0,1,0)$ is a model of a Boolean formula $F$, whereas $(0,0,0)$ is not. SAT asks for existence of at least one satisfying assignment, rather than for every Boolean valuation to work; the latter condition makes $F$ a tautology.