Even Harder Extra PL Translations--Solutions

1. Every administrator earns more than some faculty member, and every faculty member earns more than some administrator.

x[Ax y( Fy & Exy )] &x[Fx y( Ay & Exy )]

2. If any administrator earns more than every faculty member, Jones does.

x[Ax &y( Fy Exy )] y( Fy Ejy )

3. No faculty member earns more than the president.

~y( Fy & Eyp )

4. Any administrator who earns more than every faculty member should be fired.

x{[Ax &y( Fy Exy )] Rx }

5. No faculty member earns more than the president, but some coaches do.

~y( Fy & Eyp ) &y( Cy & Eyp )

6. There is an administrator who is a faculty member and is distrusted by all administrators who are not faculty members.

x[(Ax & Fx ) &y{(Ay & ~Fy) Dyx }]

7. Every faculty member who is an M.D. earns more than every faculty member who is not an M.D.

x{[Fx & Mx] y[( Fy & ~My) Exy ]}

8. Every faculty member who is an administrator earns more than some faculty members who are not administrators.

x{[Fx & Ax] y[( Fy & ~Ay) & Exy ]}

9. At least one administrator who is not a faculty member earns more than every faculty member who is not an administrator.

x{[~Fx & Ax] &y[( Fy & ~Ay) Exy ]}

10. No professor bores every student who enrolls in some class the professor teaches.

~x( Px &y{( Sy &z[(Cz & Txz) & Eyz ]) Bxy })

11. Some faculty members distrust every administrator and some administrators distrust every faculty member.

x[Fx &y( Ay Dxy )] &x[Ax &y( Fy Dxy )]

12. Some faculty member who is distrusted by some administrator is respected by every faculty member not distrusted by some administrator.

x([Fx &y( Ay & Dyx )] &y{[ Fy &z(Az & ~Dzy)] Ryx })

13. Anyone who distrusts everyone is either paranoid or an administrator or a union officer.

x{yDxy [Px v ( Ax v Ux )]}

14. Everyone distrusts someone, but only administrators who are not faculty members distrust everyone.

xyDxy & ~x[( ~Ax & ~Fx ) &yDxy ]

15. Professors don't understand the students they bore, and students don't listen to the professors they are bored by.

x[Px y{( Sy & Bxy) ~Uxy }] &x[Sx y{( Py & Byx) ~Lxy }]