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Why is truth table enumeration impractical for large problems?

  • A.The method gives no proof, only a yes or no answer
  • B.Truth tables apply only to sentences without negation
  • C.The number of models grows exponentially with the symbols
  • D.Truth tables cannot represent implication correctly

Answer: C

With two to the n models, a problem with fifty symbols has more rows than could be enumerated in the age of the universe, so satisfiability solvers search cleverly instead. Implication and negation are handled correctly, and the absence of a proof is a separate objection. A definition that is exponentially large, and an algorithm that must avoid materialising it, is the shape of the whole subject of automated reasoning.

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