Symbolization Exercises Involving Monadic Predicates and Multiple Quantification

These exercises are taken from Irving Copi, Symbolic Logic, fifth edition, Macmillan, 1979.

Symbolize each of the following English sentences using the dictionary suggested and multiple quantifiers where necessary.

  1. If anything is damaged, someone will be blamed. (Dx, Px, Bx)
  2. If anything is damaged, the tenant will be charged for it. (Dx, Cx)
  3. If nothing is damaged, nobody will be blamed. (Dx, Bx)
  4. If something is damaged, but nobody is blamed, the tenant will not be charged for it. (Dx, Bx, Cx)
  5. If any bananas are yellow, they are ripe.  (Bx, Yx, Rx)
  6. If any bananas are yellow, then some bananas are ripe. (Bx, Yx, Rx)
  7. If any bananas are yellow, then if all yellow bananas are ripe, they are ripe. (Bx, Yx, Rx)
  8. If all ripe bananas are yellow, some yellow things are ripe. (rx, Bx, Yx)
  9. If all officers present are either captains or majors, then either some captains are present or some majors are present. (Ox, Px, Cx, Mx)
  10. If any officer is present, then either no majors are present or he is a major. (Ox, Px, Mx)
  11. If some officers are present, then if all officers present are captains, then some captains are present. (Ox, Px, Cx)
  12. If some officers are present, then if all officers present are captains, then they are captains. (Ox, Px, Cx)
  13. If all survivors are fortunate and only women were survivors, then if there are any survivors, then some women are fortunate. (Sx, Fx, Wx)
  14. If any survivors are women, then if all women are fortunate, they are fortunate. (Sx, Wx, Fx)
  15. If there are any survivors and only women are survivors, then they are women. (Sx, Wx)
  16. If every position has a future and no employees are lazy, then some employees will be successful. (Px, Fx, Ex, Lx, Sx)
  17. If any employees are lazy, then if some positions have no future, then they will not be successful. (Ex, Lx, Px, Fx, Sx)
  18. If any employees are lazy and some positions have no future, then some employees will not be successful. ((Ex, Lx, Px, Fx, Sx)
  19. If any husband is unsuccessful, then if all wives are ambitious, then some wives will be disappointed. (Hx, Sx, Wx, Ax, Dx)
  20. If any husband is unsuccessful, then if some wives are ambitious, he will be unhappy. (Hx. Sx, Wx, Ax, Px)
SOLUTIONS                Monadic Predicate Symbolization Exercises with Multiple Quantification