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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 $\exists^{1}$ to mean “there exists exactly one.”)

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

  2. Joan has exactly one daughter (but may have sons as well).

  3. Joan has exactly one child, a daughter.

  4. Joan and Kevin have exactly one child together.

  5. Joan has at least one child with Kevin, and no children with anyone else.