$4.$ For this exercise, use the following sets and predicates:

P $=$ a set of $$people$$

ParentOf$($p$,$ c$)=$p is a parent of c$$ where p$,$ c in P

SiblingOf$($p$,$ q$)=$p and q are siblings$($symmetric$)$ where p$,$ q in P

CloseRel$($p$,$ q$)=$p and q are closely related$($symmetric$)$ where p$,$ q in P

Translate each of the following statements into propositions in predicate logic using the appropriate

quantifiers:

$($a$)$ A person is closely related to their parent.

$($b$)$ If two people are siblings, they are closely related.

$($c$)$ Every person has at least one other person they are closely related to$.$

$($d$)$ For every person, there is someone that they are not a sibling of$.$

$($e$)$ There is no person that is closely related to everyone.

$($f$)$ There are three people such that the first and second are siblings and the second and third are

siblings, but the first and third are not siblings.

$($g$)$ If two people are siblings, there is someone who is the parent of both of them.

$($h$)$ If two people are closely related, then they are siblings or one is the parent of the other.