Philosophy 251: Handout #14

XXII. Translate each of the following sentences into PL.

  1. Every administrator earns more than some faculty member, and every faculty member earns more than some administrator.
  2. No faculty member earns more than the president.
  3. Any administrator who earns more than every faculty member should be fired.
  4. No faculty member earns more than the president, but some coaches do.
  5. At least one administrator who is not a faculty member earns more than every faculty member who is not an administrator.
  6. No professor bores every student who enrolls in some class the professor teaches.
  7. Some faculty members distrust every administrator and some administrators distrust every faculty member.
  8. Any faculty member who distrusts everyone is either paranoid or an administrator or a union officer.
  9. Everyone distrusts someone, but only administrators who are not faculty members distrust everyone.
  10. Professors don't understand the students they bore, and students don't listen to the professors they are bored by.

XXIII. For each of the following arguments construct a derivation to prove that the argument is valid.

  1. Universal QuantifierxAx / Aa & Ab
  2. Universal QuantifierxUniversal QuantifieryBxy, Bcd Ce / Ce
  3. Universal Quantifierx( Dx Ex ), Universal Quantifierz( Ez Fz ) / Df Ff
  4. Universal QuantifierzGz, Universal Quantifierx~Gx / ~Hg
  5. Universal Quantifierx( Ix & ~Kx), Lh v Kj / Universal QuantifierxKx ( Ik & Lh )
  6. Ma, Na / Existential Quantifierx( Nx & Mx )
  7. Obbb / Existential QuantifieryOyby
  8. Universal QuantifierxUniversal QuantifieryPxy / Existential QuantifierwExistential QuantifierzPwz
  9. Universal QuantifierxQx, Existential QuantifierzQz Universal QuantifieryRy / Rc
  10. ~Existential QuantifierxSxx v Universal QuantifierzTz, Sdd / Universal QuantifierzUzzz v ( Te v Existential QuantifieryWy )

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