1) 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.

2) A propositional wff is a tautology if it is always true regardless of the truth values assigned to the statement letters of the proposition. The analogue to a tautology for a predicate wff is for it to be valid. A valid predicate wff is true under all possible interpretations (any domain of interpretation and meaning of associated with the predicates).

Which of the following predicate wffs are valid? For the invalid predicate wffs, describe why they are not valid.

a) where a is in the domain of interpretation

b)

c)

d)

e)

f)

g)