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Which of the following is true related to satisfiable property ?

  • A.A statement is satisfiable if there is some interpretation for which it is false
  • B.A statement is satisfiable if some interpretation for which it is true
  • C.A statement is satisfiable if there is no interpretation for which it is true
  • D.A statement is satisfiable if there is no interpretation for which it is false

Answer: B

A statement is satisfiable if there is some interpretation for which it is true.

In logic, an interpretation assigns truth values (or meanings) to the symbols. A formula is satisfiable if at least one interpretation makes it true, valid if every interpretation makes it true, and unsatisfiable if none does.

Having some interpretation in which it is false makes a formula not valid. No interpretation making it true is unsatisfiability, and no interpretation making it false is validity.

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