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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

Wffor not wff?

Get ready to play!!!




2 cube x
2. Cube(x)


Cube x
Cube(x)


Cube x1
Cube(x)

  • A quantifier must always be followed by a variable, e.g.

    y Cube(x)


3 tet x
3. Tet(x)


Tet x
Tet(x)




Smaller cube a tet b1
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)


5 z tet x cube a
5. z(Tet(x)  Cube(a))


Z tet x cube a
z(Tet(x)  Cube(a))


Z tet x cube a1
z(Tet(x)  Cube(a))

  • Order of construction:

    Tet(x)

    Cube(a)

    (Tet(x)  Cube(a))

    z(Tet(x)  Cube(a))


Z tet x cube a2
z(Tet(x)  Cube(a))


6 c large c
6. c Large(c)


C large c
c Large(c)


C large c1
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)


7 smaller a large a
7. Smaller(, a)  Large(a)


Smaller a large a
Smaller(, a)  Large(a)


Smaller a large a1
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))


8 x large x y tet y adjoins x y
8. x(Large(x) y(Tet(y)  Adjoins(x, y)))


X large x y tet y adjoins x y
x(Large(x) y(Tet(y)  Adjoins(x, y)))


X large x y tet y adjoins x y1
x(Large(x) y(Tet(y)  Adjoins(x, y)))

  • Circuit diagram:


9. Cube(a)  Large(a)  Small(y)


Cube(a)  Large(a)  Small(y)


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.)


10 y dentist father y rich y
10. y(Dentist(father(y))  Rich(y))


Y dentist father y rich y
y(Dentist(father(y))  Rich(y))


Y dentist father y rich y1
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))