Each of these statements (which are true) refers to seven out of the eight living members of a family. You will find that the statement either refers to them by their personal name or through their relationship with another member. The statements are:
a) Jacob"s wife"s sister"s husband"s mother"s son is Patrick"s cousin"s father.
b) Sia"s grand-daughter"s cousin"s father"s sister-in-law is Gerry"s son-in-law"s wife.

Now if Annabelle has no children, what relationship does she share with Michael?

PS: There can be two solutions to this problem.

Solution 1:
Annabelle is Michael"s daughter. This is because Michael is Sia"s son. Also he is married to one of the Gerry"s daughters. Gerry"s other daughter is married to Jacob and Patrick is their son.

Solution 2:
Michael and Jacob are brothers. Sia is their mother. In this case, "Jacob"s wife"s sister"s husband"s mother"s son" refers to Jacob himself. Thus, Patrick is Michale"s son and Annabelle is Jacob"s daughter which means that Annabelle is Michael"s niece.