A is the father of B. But B is not the son of A. How’s that possible?
This is the standard riddle, probably Bilbo and Gollum asked it one to another :)
It exploits our languages' historical sexism: somebody is by default he. Especially if "he" father has been mentioned already. Also a human being is called "a man" in English.
But "me, your father" may have not only sons, but also daughters. So the answer for this situation is "B is the daughter of A".
Let's consider this situation from the point of view of mathematics (functions, mappings). Denote the set of all people (live or not) as P and define the function F from P to P, F(human) = the farther of this human. This function is defined for every human from P, but it has no inverse function, because not every human is somebody's father.
The statement offers a reasoning challenge by presenting arguments that may easily lead to the development of a fallacy. Focus on the letters A and B may divert one's concentration from the terminology used. In the second sentence, the term son and not child has been used. Thus, gender has been introduced into the reasoning challenge, meaning that gender considerations should be employed towards answering the question. In this case, A is the father of B, making B his child. Additionally, B can either be a boy or a girl. Thus, if the child is not a son then it is definitely a girl, meaning B is A’s daughter. A fallacy in this instance would be to assume that B or the child has to be a boy.