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What is wrong with writing all students are diligent using conjunction?

  • A.It claims some student is not diligent
  • B.It is satisfied by any object that is not a student
  • C.It cannot be evaluated in a finite domain
  • D.It claims every object in the domain is a student

Answer: D

Writing for every x, x is a student and x is diligent asserts that everything whatever is a student, which is far stronger than intended. The third option describes the error made by using implication with the existential quantifier instead. Finiteness is irrelevant. Working out what the wrong formula actually says, rather than merely noting that it is wrong, is what prevents the error from recurring.

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