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Which implication holds between the two quantifier orders?

  • A.Neither order implies the other in general
  • B.The two orders are logically equivalent
  • C.Exists then forall implies forall then exists
  • D.Forall then exists implies exists then forall

Answer: C

If one individual loves everybody then certainly everybody is loved by someone, but the converse fails since each person might be loved by a different individual. The stronger claim implies the weaker. Working out which of two similar formulas is stronger, by finding a model of one that is not a model of the other, is the standard technique for settling such questions and it is more reliable than intuition.

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