More Symbolization Exercises Using Monadic Predicates and Single Quantification

Use the following dictionary and symbolize each of the following sentences

  1. Some horses are gentle and have been well trained.

  2. Some horses are gentle only if they have been well trained.

  3. Some horses are gentle if they have been well trained.

  4. Any horse is gentle that has been well trained.

  5. Any horse that is gentle has been well trained.

  6. No horse is gentle unless it has been well trained.

  7. Any horse is gentle if it has been well trained.

  8. Any horse has been well trained if it is gentle.

  9. Any horse is gentle if an only if it has been well trained.

  10. Gentle horses have all been well trained.

  11. Only well trained horses are gentle.

  12. Only gentle horses have been well trained.

  13. Some horses are gentle even though they have not been well trained.

  14. If something is a well trained horse, then it must be gentle.

  15. Some horses that are well trained are not gentle.

  16. Some horses are neither gentle nor well trained.

  17. No horse that is well trained fails to be gentle.

  18. A horse is gentle only if it has been well trained.

  19. If anything is a gentle horse, then it has been well trained. 

  20. If any horse is well trained, then it is gentle. 

SOLUTIONS