Wff or not a wff?

Wff or not wff?Get ready to play!!!11. Cube(a)2Cube(a)

32. Cube(x)4Cube(x)

5Cube(x)A quantifier must always be followed by a variable, e.g.

y Cube(x)63. Tet(x)7

Tet(x)

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

10Smaller(Cube(a), Tet(b))The only things you can put into a predicate hole are a name, a variable, or a function.You cant put a predicate into another predicate. In this case you need to write:

(Cube(a) Tet(b)) Smaller(a, b)115. z(Tet(x) Cube(a))

12z(Tet(x) Cube(a))

13z(Tet(x) Cube(a))Order of construction:

Tet(x)Cube(a) (Tet(x) Cube(a))z(Tet(x) Cube(a))14z(Tet(x) Cube(a))

156. c Large(c)

16c Large(c)

17c 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)187. Smaller(, a) Large(a)19

Smaller(, a) Large(a)

20Smaller(, a) Large(a)The only things you can put into a predicate hole are a name, a variable, or a function.You cant put a quantifier directly into the hole of a predicate. In this case you need:

x (Smaller(x, a) Large(a))

218. x(Large(x) y(Tet(y) Adjoins(x, y)))22x(Large(x) y(Tet(y) Adjoins(x, y)))

23x(Large(x) y(Tet(y) Adjoins(x, y)))Circuit diagram:

249. Cube(a) Large(a) Small(y)

25Cube(a) Large(a) Small(y)

26Cube(a) Large(a) Small(y)

You need to add brackets when using and . Then, depending on the order of construction, youll get either:

(Cube(a) Large(a)) Small(y) orCube(a) (Large(a) Small(y))

(I left off the outer pair of brackets, as usual.)2710. y(Dentist(father(y)) Rich(y))28y(Dentist(father(y)) Rich(y))

29y(Dentist(father(y)) Rich(y))Order of construction:

Dentist(father(y))Rich(y)(Dentist(father(y)) Rich(y))y(Dentist(father(y)) Rich(y))30