Assuming predicates parent(P, Q) and female(P) and constants joan and kevin, with the obvious meanings, express each of the following sentences in first-order logic. (You may use the abbreviation 1 to mean there exists exactly one.)

a. joan has a daughter (possibly more than one, and possibly sons as well).

b. joan has exactly one daughter (but may have sons as well).

c. joan has exactly one child, a daughter.

d. joan and kevin have exactly one child together.

e. joan has at least one child with kevin, and no children with anyone else.