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Why is implication eliminated during conversion to clausal form?

  • A.The elimination reduces the size of the formula
  • B.Clauses are built from disjunction and negation only
  • C.Implication has no truth table in propositional logic
  • D.Implication cannot be nested inside other connectives

Answer: B

A clause is a disjunction of literals, so every connective must first be rewritten in terms of negation, conjunction and disjunction, and the implication rewrite is the first step. Implication is perfectly truth functional and may be nested freely, and the rewrite generally leaves the size unchanged. Reducing a rich syntax to a minimal one, so that a single inference rule suffices, is the purpose of the whole conversion.

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