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Wff or not wff? Get ready to play!!!

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1. Cube(a)

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Cube(a)

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2. Cube(x)

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Cube(x)

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

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3. Tet(x)

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Tet(x)

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

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

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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)

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5. z(Tet(x) Cube(a))

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z(Tet(x) Cube(a))

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

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6. c Large(c)

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c Large(c)

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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)

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7. Smaller( , a) Large(a)

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Smaller( , a) Large(a)

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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))

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8. x(Large(x) y(Tet(y) Adjoins(x, y)))

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x(Large(x) y(Tet(y) Adjoins(x, y)))

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Circuit diagram:

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

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

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

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10. y(Dentist(father(y)) Rich(y))

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

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