“$ x $ is a brother of $ y $.” Why is this not transitive? I am working on a problem set at the moment, and while checking my answers I realized that I have listed "x is a brother of y" as a transitive relation, while the answers say that it is not. 

EDIT: I realized I forgot to put some assumptions from the question: 
i) Domain is people in general.
ii) Assume that all siblings share both parents.

But if x is a brother of y, and y is a brother of z, then surely x is a brother of z? Am I missing something here? 

Please help a student out. Thanks!
If Fred is Bob's brother, and vice versa, transitivity would imply that Fred is his own brother.
What if Y is female.  So X is a brother of Y, but Y is a sister of X.