1) What is the truth value of each of the following wffs where the domain of interpretation for x and y are integers?

a)

b)

c)

d)

2) What is the scope of each quantifier in the wff ?

3) What is the truth value of the wff

in the interpretation where the domain consists of all integers, A(x) is "x > 0," B(x, y) is "x > y," and C(y) is

""?

4) The English sentence

"Every cat has fleas."

translates to predicate logic as

, where C(x) is "x is a cat" and F(x) is "x has fleas."

For the English sentence

"There is a cat that has fleas."

why is the predicate logic translation

, where C(x) is "x is a cat" and F(x) is "x has fleas."

incorrect?

5) Using the predicate symbols shown and the appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.)

J(x) is "x is a judge."

C(x) is "x is a chemist."

L(x) is "x is a lawyer." A(x, y) is "x admires y."
W(x) is "x is woman."  

a. There are some women lawyers who are chemists.

b. No woman is both a lawyer and a chemist.

c. Some lawyers admire only judges.

d. All judges admire judges.

e. Only judges admire judges.

f. All women lawyers admire some judges.

g. Some women admire no lawyer.