. . . . . . . 1.) The sentence

Some dogs eat vegetables.

is equivalent to

There are animals, which are dogs and eat vegetables.

is equivalent to

$ (\exists x)(Q(x) \wedge P(x))$ .


. . . . . . . 2.) The sentence

All dogs chase cars.

is equivalent to

If an animal is a dog, then it chases cars.

is equivalent to

$ (\forall x)(Q(x) \Rightarrow R(x))$ .


. . . . . . . 3.) The sentence

No dogs chase cars.

is equivalent to

If an anmial is a dog, then it does not chase cars.

is equivalent to

$ (\forall x)(Q(x) \Rightarrow ( \sim R(x)) $

or (by Theorem 1.1 a.)

$ (\forall x)(R(x) \Rightarrow ( \sim Q(x)) $ .


. . . . . . . 4.) The sentence

There are some animals which chase cars but do not eat vegetables.

is equivalent to

$ (\exists x)(R(x) \wedge ( \sim P(x)) $ .



RETURN to problem set.



Duane Kouba 2002-06-06