A formula is satisfiable when at least one assignment makes it true. If an exact counter returns #F, answer YES when #F > 0 (at least one assignment works) and NO when #F = 0. Thus an exact counting procedure can also answer the satisfiability question. A single YES answer does not, in general, reveal how many assignments work or provide their values. A faster counting claim still needs a justified running-time analysis; this logical connection supplies no speed guarantee by itself.