$($ii$))>(C$

$($iii$)))=>((E$

b$.$ Which of the sentences in $($a$)$ can be expressed in Horn form?

$6.$ Which of the following are correct?

a$.$ False $||==$ True.

b$.$ True $||==$ False.

c$.(A^{{?}^{?}}B)||)>(B.$

d$.A>B||==$AvvB.

e$.A>B||==$notAvvB.

f$.(A^{{?}^{?}}B)=>C||)=>(C)=>(C.$

g$.))=>(C)=>((C.$

h$.(AvvB{)}^{{?}^{?}}(notCvvnotDvvE)||==(AvvB).$

i$.(AvvB{)}^{{?}^{?}}(notCvvnotDvvE)||==(AvvB{)}^{{?}^{?}}(notDvvE).$

j$.)=>(B$ is satisfiable.

k$.)>(B$ is satisfiable.

l$.)>(B$ has the same number of models as $)>(B$ for any fixed set of proposition symbols that includes $A,B,C.$

$7.$ Consider a vocabulary with the following symbols:

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

Customer$($p$1,$ p$2)$: Predicate. Person p$1$ is a customer of person p$2.$

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:

a$.$ Emily is either a surgeon or a lawyer.

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

c$.$ All surgeons are doctors.

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

e$.$ Emily has a boss who is a lawyer.