Artificial intelligent assistant

Reasoning ( CSIR NET December 2015) This question was asked in CSIR NET December 2015. I could not solve this question.Although I know the answer that CSIR posted in their answer key, which is 2. But I cannot understand how 2 is the correct option. Please help to solve this question. The statement: “ **The father of my son is the only child of your parents** ” 1. can never be true 2. is true in only one type of relation 3. can be true for more than one type of relations 4. can be true only in a polygamous family.

Speaker is a mother and the father is being spoken to if we disregard other sexual orientations.

Suppose $x$ is the speaker and $y$ is being spoken to. $x$ must be a parent. Suppose $x$ is the father. Then $x$ is referring to himself as he says "father of my son". So $x$ is the only child of $y$'s parents i.e. $x=y$ and $x$ is talking to himself. Therefore $x$ can't be the father $\implies x$ is the mother. Now the only child of $y$'s parents is $y$. So $y$ is the father.

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