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Which connective naturally accompanies the universal quantifier?

  • A.Negation
  • B.Implication
  • C.Conjunction, since every case must hold together
  • D.Disjunction, since any of the cases may hold

Answer: B

Saying that all students are diligent is written as: for every object, if it is a student then it is diligent, since using conjunction would claim that every object in the domain is a student. That error is among the two commonest in translating English into logic. Disjunction and negation have their own uses. The pairing of universal with implication, and existential with conjunction, is worth learning as a rule because both errors produce formulas that look plausible.

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