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What is a satisfiable sentence?

  • A.One true in every model without exception
  • B.One that can be derived from the empty set of premises
  • C.One whose negation is also satisfiable
  • D.One true in at least one model

Answer: D

Satisfiability requires only that some assignment makes the sentence true, which is a far weaker demand than validity. A sentence is valid exactly when its negation is unsatisfiable, which is the relationship every proof by refutation exploits. Derivability from nothing is validity in a complete system, and the negation of a satisfiable sentence may or may not be satisfiable. The three notions are connected by negation, and knowing the connections converts one question into another that may be easier.

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