Exercise A

Using the following symbolization key:

• domain:

  people

• $K(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ knows the combination to the safe

• $S(x)$:

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

• $V(x)$:

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

• $T(x,y)$:

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

• $h$:

  Hofthor

• $i$:

  Ingmar

symbolize the following sentences in FOL:

1. Hofthor trusts a vegetarian.

2. Everyone who trusts Ingmar trusts a vegetarian.

3. Everyone who trusts Ingmar trusts someone who trusts a vegetarian.

4. Only Ingmar knows the combination to the safe.

5. Ingmar trusts Hofthor, but no one else.

6. The person who knows the combination to the safe is a vegetarian.

7. The person who knows the combination to the safe is not a spy.