Extra PL Translations--Answers

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1. Someone is respected by everyone.

Existential QuantifierxUniversal QuantifieryRyx


2. Kilroy was here.

Hk


3. Onyx is a cat.

Co


4. Neither Onyx nor Hypatia is fat.

~( Fo v Fh )


5. Cyrano loves Roxanne.

Lcr


6. Philosophers dislike politicians.

Universal Quantifierx( Px Universal Quantifiery ( Cy Dxy ))


7. Romulans are crafty, but Klingons are dangerous.

Universal Quantifierx( Rx Cx ) & Universal Quantifierx( Kx Dx )


8. Christian wins Roxanne only if Cyrano helps him.

Wcr Hnc


9. Freshmen and sophomores are eligible, but juniors are not.

Universal Quantifierx[( Fx v Sx ) Ex ] &Universal Quantifierx( Jx ~Ex )


10. Everyone is taller than Desdemona.

Universal QuantifierxTxd


11. If nothing is impossible, then anything is possible.

~Existential Quantifierx~Px Universal QuantifierxPx


12. Nothing works unless nothing is broken.

~~Existential QuantifierxBx ~Existential QuantifierxWx


13. Professors like diligent students.

Universal Quantifierx( Px Universal Quantifiery[( Dy & Sy ) Lxy ])


14. If anyone is captain, then no Vulcan is.

Existential QuantifierxCx ~Existential Quantifierx( Vx & Cx )


15. Everything is mortal or immortal and any worshipped deity is immortal.

Universal Quantifierx( Mx v ~Mx ) &Universal Quantifierx[( Wx & Dx ) ~Mx ]


16. Only gods are immortal only if every human is mortal.

~Existential Quantifierx( ~Gx & ~Mx ) Universal Quantifierx( Hx Mx )


17. The only dangerous pets are spiders or snakes.

Universal Quantifierx[( Dx & Px ) ( Sx v Kx )]


18. No one who has survived a shipwreck is not protected by Neptune.

~Existential Quantifierx[Existential Quantifiery( Wy & Sxy ) & ~Pnx ]


19. All students like some professor who likes them.

Universal Quantifierx( Sx Existential Quantifiery[( Py & Lyx ) & Lxy ])


20. No cat wants any dog unless every dog has a mouse.

~Universal Quantifierx( Dx Existential Quantifiery( My & Hxy )) ~Existential Quantifierx( Cx &Existential Quantifiery( Dy & Wxy ))


21. Every gangster is feared by some obsequious lackey.

Universal Quantifierx( Gx Existential Quantifiery[( Oy & Ly ) & Fyx ])


22. There are no unspeakable truths.

~Existential Quantifierx( ~Sx & Tx )


23. All cows are sacred or all cows fly.

Universal Quantifierx( Cx Sx ) vUniversal Quantifierx( Cx Fx )


24. Anyone who lives in an apartment is a senior.

Universal Quantifierx(Existential Quantifiery( Ay & Lxy ) Sx )


25. George does not like anyone, but everyone likes George.

~Existential QuantifierxLgx &Universal QuantifierxLxg


26. Someone who is lying hates anyone who always tells the truth.

Existential Quantifierx[Lx &Universal Quantifiery( Ty Hxy )]


27. No overpaid player does not play for the Bulls.

~Existential Quantifierx[( Ox & Px ) & ~Lxb ]


28. Riker is liked by no one, unless he defeats all Romulans.

~Universal Quantifierx( Rx Drx ) ~Existential QuantifieryLyr


29. Some students are failing every class they have, but some are not.

Existential Quantifierx( Sx &Universal Quantifiery[( Cy & Hxy ) Fxy ]) &Existential Quantifierx( Sx & ~Universal Quantifiery[( Cy & Hxy ) Fxy ])


30. Only those not beyond suspicion are lying.

~Existential Quantifierx( Bx & Lx )


31. If the universe began, then the universe will end.

Bu Eu


32. If a spy is nearby, then no one is safe.

Existential Quantifierx( Sx & Nx ) ~Existential QuantifierxFx


33. Every play written by Shakespeare is better than any movie.

Universal Quantifierx[( Px & Wsx ) Universal Quantifiery( My Bxy )]


34. Since no electron has positive charge, nothing with positive charge is an electron.

~Existential Quantifierx( Ex & Px ) ~Existential Quantifierx( Px & Ex )


35. Some pets are not cats or dogs.

Existential Quantifierx( Px & ~( Cx v Dx ))


36. Only mistakes make Mike mad.

~Existential Quantifierx(~Mx & Dxm )


37. The only rich soccer players are good athletes or obnoxious snobs.

Universal Quantifierx{( Rx & Sx ) [( Gx & Ax ) v ( Ox & Nx )]}


38. Everything is sacred unless someone is despicable, in which case nothing is sacred.

( ~Existential QuantifierxDx Universal QuantifierxSx ) & (Existential QuantifierxDx ~Existential QuantifierxSx )


39. No student has read every book in the library.

~Existential Quantifierx( Sx &Universal Quantifiery[( By & Iyl ) Rxy ])


40. No evil act shall go unpunished.

~Existential Quantifierx[( Ex & Ax ) & ~Px ]


41. Dinosaurs and birds have a common ancestor.

Universal QuantifierxUniversal Quantifiery[( Dx & By ) Existential Quantifierz( Azx & Azy )]


42. Demanding professors challenge all of their students.

Universal Quantifierx[( Dx & Px ) Universal Quantifiery( Syx Cxy )]


43. Everyone who respects oneself is respected by everyone who respects someone.

Universal Quantifierx[ Rxx Universal Quantifiery(Existential QuantifierzRyz Ryx )]


44. Not everyone is incorruptible if and only if the only role models are corruptible.

~Universal Quantifierx~Cx Universal Quantifierx( Rx Cx )


45. Bill is president and Bob is not.

Pb & ~Po


46. Diligent students who study hard and like all their professors always pass.

Universal Quantifierx({[( Dx & Sx ) & Hx ] &Universal Quantifiery(Pyx Lxy )} Ax )


47. No student who does not respect him or herself is respected by every student.

~Existential Quantifierx[( Sx & ~Rxx ) &Universal Quantifiery( Sy Ryx )]


48. If anyone likes anyone who loves no one, then he or she loves no one too.

Universal Quantifierx[Existential Quantifiery( ~Existential QuantifierzLyz & Kxy ) ~Existential QuantifierzLxz ]


49. Anyone taller than Tim is taller than every basketball player shorter than the tallest jockey.

Universal Quantifierx{ Txt Universal Quantifiery[( By & Syj) Txy ]}


50. Everyone has reached the end.

Universal QuantifierxRxe

 

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