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Wff or not wff ?

Wff or not wff ?. Get ready to play!!!. 1. Cube(a). Cube(a). 2.  Cube(x).  Cube(x).  Cube(x). A quantifier must always be followed by a variable, e.g. y Cube(x). 3. Tet (x). Tet (x). 4. Smaller(Cube(a), Tet (b)). Smaller(Cube(a), Tet (b)). Smaller(Cube(a), Tet (b)).

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Wff or not wff ?

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  1. Wffor not wff? Get ready to play!!!

  2. 1. Cube(a)

  3. Cube(a)

  4. 2. Cube(x)

  5. Cube(x)

  6. Cube(x) • A quantifier must always be followed by a variable, e.g. y Cube(x)

  7. 3. Tet(x)

  8. Tet(x)

  9. 4. Smaller(Cube(a), Tet(b))

  10. Smaller(Cube(a), Tet(b))

  11. Smaller(Cube(a), Tet(b)) • The only things you can put into a predicate hole are a name, a variable, or a function. • You can’t put a predicate into another predicate. In this case you need to write: (Cube(a)  Tet(b))  Smaller(a, b)

  12. 5. z(Tet(x)  Cube(a))

  13. z(Tet(x)  Cube(a))

  14. z(Tet(x)  Cube(a)) • Order of construction: Tet(x) Cube(a) (Tet(x)  Cube(a)) z(Tet(x)  Cube(a))

  15. z(Tet(x)  Cube(a))

  16. 6. c Large(c)

  17. c Large(c)

  18. c Large(c) A quantifier must be followed by a variable, i.e. one of the letters: t, u, v, w, x, y, z. So you need (e.g.): v Large(v)

  19. 7. Smaller(, a)  Large(a)

  20. Smaller(, a)  Large(a)

  21. Smaller(, a)  Large(a) • The only things you can put into a predicate hole are a name, a variable, or a function. • You can’t put a quantifier directly into the hole of a predicate. In this case you need: x (Smaller(x, a)  Large(a))

  22. 8. x(Large(x) y(Tet(y)  Adjoins(x, y)))

  23. x(Large(x) y(Tet(y)  Adjoins(x, y)))

  24. x(Large(x) y(Tet(y)  Adjoins(x, y))) • Circuit diagram:

  25. 9. Cube(a)  Large(a)  Small(y)

  26. Cube(a)  Large(a)  Small(y)

  27. Cube(a)  Large(a)  Small(y) • You need to add brackets when using  and . Then, depending on the order of construction, you’ll get either: (Cube(a)  Large(a)) Small(y) or Cube(a) (Large(a)  Small(y)) • (I left off the outer pair of brackets, as usual.)

  28. 10. y(Dentist(father(y))  Rich(y))

  29. y(Dentist(father(y))  Rich(y))

  30. y(Dentist(father(y))  Rich(y)) • Order of construction: Dentist(father(y)) Rich(y) (Dentist(father(y))  Rich(y)) y(Dentist(father(y))  Rich(y))

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