**Unit 4: Logic** (Assignment 4, answers by: A.Aziz Altowayan)

**Exercise 8.9** (answers in red)

**Exercise 8.10**

Emily is either a surgeon or a lawyer.

*O**c**c**u**p**a**t**i**o**n*(*E**m**i**l**y*,*S**u**r**g**e**o**n*) ∨*O**c**c**u**p**a**t**i**o**n*(*E**m**i**l**y*,*L**a**w**y**e**r*)Joe is an actor, but he also holds another job.

*O**c**c**u**p**a**t**i**o**n*(*J**o**e*,*A**c**t**o**r*) ∧ ∃*o**o*≠*A**c**t**o**r*∧*O**c**c**u**p**a**t**i**o**n*(*J**o**e*,*o*)All surgeons are doctors.

∀*x**O**c**c**u**p**a**t**i**o**n*(*x*,*S**u**r**g**e**o**n*) ⇒*O**c**c**u**p**a**t**i**o**n*(*x*,*D**o**c**t**o**r*) ≡ ∀*x**S**u**r**g**e**o**n*(*x*) ⇒*D**o**c**t**o**r*(*x*)Joe does not have a lawyer (i.e., is not a customer of any lawyer).

¬*C**u**s**t**o**m**e**r*(*J**o**e*,*L**a**w**y**e**r*)Emily has a boss who is a lawyer.

∃*x**B**o**s**s*(*x*,*E**m**i**l**y*) ⇒*O**c**c**u**p**a**t**i**o**n*(*x*,*L**a**w**y**e**r*) ≡ ∃*x**B**o**s**s*(*x*,*E**m**i**l**y*) ∧*O**c**c**u**p**a**t**i**o**n*(*x*,*L**a**w**y**e**r*)There exists a lawyer all of whose customers are doctors.

∃*x**O**c**c**u**p**a**t**i**o**n*(*x*,*L**a**w**y**e**r*) ∧ ∀*y**C**u**s**t**o**m**e**r*(*y*,*x*) ⇒*O**c**c**u**p**a**t**i**o**n*(*y*,*D**o**c**t**o**r*)Every surgeon has a lawyer.

∀*x**O**c**c**u**p**a**t**i**o**n*(*x*,*S**u**r**g**e**o**n*) ∧ ∃*y**C**u**s**t**o**m**e**r*(*x*,*y*) ≡ ∀*x**O**c**c**u**p**a**t**i**o**n*(*x*,*S**u**r**g**e**o**n*) ⇒ ∃*y**C**u**s**t**o**m**e**r*(*x*,*O**c**c**u**p**a**t**i**o**n*(*y*,*L**a**w**e**r*))^{ * }

*`complex sentence syntax`