Quantifiers

By using the apparatus of variables, predicates, and quantifiers, we can make statements of any complexity. We are not limited to two terms, as in classical logic. Here is an example:

All banks that are chartered by the federal government can borrow from the Federal Reserve System.

(x)[(Bx Cx) Fx]


Comprehension Questions

1 Which of the following is the correct symbolization of "All S are P?"
a) (x)(Sx.~Px)
b) (x)(Sx>~Px)
c) (x)(Sx.Px)
d) (x)(Sx>Px)
2 Which of the following is the correct symbolization of "No S is P?"
a) (x)(Sx.~Px)
b) (x)(Sx>~Px)
c) (x)(Sx.Px)
d) (x)(Sx>Px)
3 Which of the following is the correct symbolization of "Some S are P?"
a) (x)(Sx.~Px)
b) (x)(Sx>~Px)
c) (x)(Sx.Px)
d) (x)(Sx>Px)
4 Which of the following is the correct symbolization of "Some S are not P?"
a) (x)(Sx.~Px)
b) (x)(Sx>~Px)
c) (x)(Sx.Px)
d) (x)(Sx>Px)
5 Which of the following is the correct symbolization of "All teachers are dedicated?"
a) (x) (Tx > Dx)
b) (x) (Tx . Dx)
c) (x) (Tx > Dx)
d) (x) (Tx v Dx)
6 Which of the following is the correct symbolization of "Some examinations are difficult?"
a) (x) (x > Dx)
b) (x) (x > Dx)
c) (x) (x . Dx)
d) (x) (x . Dx)
7 Which of the following is the correct symbolization of "Some dogs are not vicious?"
a) (x) (Dx > ~Vx)
b) (x) (Dx . ~Vx)
c) (x) (Dx . Vx)
d) (x) (Dx . Vx)
8 Which of the following is the correct symbolization of "No man is an island?"
a) (x) (Mx > ~Ix)
b) (x) (Mx > ~Ix)
c) (x) (Mx > Ix)
d) (x) (Mx . ~Ix)


Singular statements | General statements

Existential import

© Copyright 1998, W.W. Norton & Co.