Exercise 8.11

Consider a vocabulary with the following symbols:

${Occupation}(p,o)$: Predicate. Person $p$ has occupation $o$.

${Customer}(p1,p2)$: Predicate. Person $p1$ is a customer of person $p2$.

${Boss}(p1,p2)$: Predicate. Person $p1$ is a boss of person $p2$.

${Doctor}$, $ {Surgeon}$, $ {Lawyer}$, $ {Actor}$: Constants denoting occupations.

${Emily}$, $ {Joe}$: Constants denoting people.

Use these symbols to write the following assertions in first-order logic:

1. Emily is either a surgeon or a lawyer.

2. Joe is an actor, but he also holds another job.

3. All surgeons are doctors.

4. Joe does not have a lawyer (i.e., is not a customer of any lawyer).

5. Emily has a boss who is a lawyer.

6. There exists a lawyer all of whose customers are doctors.

7. Every surgeon has a lawyer.