Exercise D

Using the following symbolization key:

• domain:

  people and dishes at a potluck

• $R(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ has run out

• $T(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is on the table

• $F(x)$:

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

• $P(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a person

• $L(x,y)$:

  $\underline{\hskip 15.00002pt}_{x}$ likes $\underline{\hskip 15.00002pt}_{y}$

• $e$:

  Eli

• $f$:

  Francesca

• $g$:

  the guacamole

symbolize the following English sentences in FOL:

1. All the food is on the table.

2. If the guacamole has not run out, then it is on the table.

3. Everyone likes the guacamole.

4. If anyone likes the guacamole, then Eli does.

5. Francesca only likes the dishes that have run out.

6. Francesca likes no one, and no one likes Francesca.

7. Eli likes anyone who likes the guacamole.

8. Eli likes anyone who likes the people that he likes.

9. If there is a person on the table already, then all of the food must have run out.