Pointing to a woman, a man says, "Her father is the only son of my father." In this blood relation question, how is the man related to the woman?

Introduction / Context:
This problem involves a man who identifies a relationship through the phrase "the only son of my father." We must determine how he is related to the woman he is pointing at. The key idea is recognizing that if someone is the only son of a father, and the speaker is that father's son, then the only son must be the speaker himself. That leads directly to the conclusion that he is the father of the woman.

Given Data / Assumptions:
• A man is pointing to a woman.• He says, "Her father is the only son of my father."• The only son of his father is a unique male child.• The speaker is one of the sons of that father.• Normal family structure is assumed.

Concept / Approach:
If the speaker's father has only one son and the speaker is that father's son, then the only son must be the speaker himself. When he says her father is the only son of my father, he is effectively saying that he himself is the woman's father. Hence we can directly conclude that the man is the father of the woman, and the woman is his daughter.

Step-by-Step Solution:
Step 1: Let F be the father of the man.Step 2: The man states that F has only one son.Step 3: The speaker is a son of F, so he must be that only son.Step 4: The sentence "her father is the only son of my father" then becomes "her father is me."Step 5: Therefore, the man is the woman's father.Step 6: Consequently, the relationship of the man to the woman is father.

Verification / Alternative Check:
Picture a family where the father has just one son. That son is the man speaking. He has a daughter, who is the woman he points to. He then truthfully can say, her father is the only son of my father. There is no possible way for him to be a brother, uncle or grandfather without contradicting the only son condition.

Why Other Options Are Wrong:
Brother of the woman: This would require at least two sons of the same father, contradicting the only son condition.Uncle of the woman: An uncle would be a brother of her parent, not the same person as her father.Brother in law of the woman: This would involve marriage, not a direct parent child relationship.Grandfather of the woman: A grandfather would be the father of her father, not her father himself.

Common Pitfalls:
Some candidates misread my father as my grandfather or overlook the phrase only son, which is crucial. Others think the only son might refer to a different son, but by definition there can be only one, and the speaker is clearly that son. Keeping the logic strict makes the answer straightforward.

Final Answer:
The man is the father of the woman.