Quantifiers in Logic
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Questions and Answers

What does the universal quantifier express in the first order formula $\forall x P(x)$?

  • Something in the domain satisfies the property denoted by $P$
  • There exists something in the domain which satisfies the property denoted by $P$
  • Nothing in the domain satisfies the property denoted by $P$
  • Everything in the domain satisfies the property denoted by $P$ (correct)

    • What is the existential quantifier in the formula $\exists x P(x)$ expressing?

  • Nothing in the domain satisfies the property denoted by $P$
  • There exists something in the domain which satisfies the property denoted by $P$ (correct)
  • Everything in the domain satisfies the property denoted by $P$
  • Something in the domain satisfies the property denoted by $P$

    • What is a formula called when a quantifier takes widest scope?

  • Negated formula
  • Quantified formula (correct)
  • Bound formula
  • Universal formula

    • Which quantifiers are standardly defined as duals in classical logic?

    <p>$\forall$ and $\exists$</p> Signup and view all the answers

    What does the formula $\neg \exists x P(x)$ express?

    <p>Nothing has the property denoted by $P$</p> Signup and view all the answers

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