Exercise E

Using the following symbolization key:

• domain:

  people

• $D(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ dances ballet

• $F(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is female

• $M(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is male

• $C(x,y)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a child of $\underline{\hskip 15.00002pt}_{y}$

• $S(x,y)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a sibling of $\underline{\hskip 15.00002pt}_{y}$

• $e$:

  Elmer

• $j$:

  Jane

• $p$:

  Patrick

symbolize the following sentences in FOL:

1. All of Patrick’s children are ballet dancers.

2. Jane is Patrick’s daughter.

3. Patrick has a daughter.

4. Jane is an only child.

5. All of Patrick’s sons dance ballet.

6. Patrick has no sons.

7. Jane is Elmer’s niece.

8. Patrick is Elmer’s brother.

9. Patrick’s brothers have no children.

10. Jane is an aunt.

11. Everyone who dances ballet has a brother who also dances ballet.

12. Every woman who dances ballet is the child of someone who dances ballet.