Introducing a man to her husband, a woman said, ‘his brother’s father is the…

Concept: In blood-relation puzzles, a person and their brother are treated as full siblings who share the same father (the convention this puzzle genre uses unless stated otherwise), so a person's brother's father is simply that person's own father. Also, “the only son of someone's paternal grandfather” identifies that someone's own father directly — a family with exactly one son in that generation leaves no other candidate for the role.

Application:

1. The woman says: the man's brother's father is the only son of my paternal grandfather.

2. Her grandfather has only one son, so that son must be the woman's own father.

3. The man's brother shares the man's father, so "the man's brother's father" is simply the man's own father.

4. Both phrases describe the same person, so the man's father equals the woman's father.

5. Two people who share the same father are siblings, so the woman and the man are siblings.

Cross-check: If the woman is the man's sister, her father is also his father. Her grandfather's only son is then her father, and separately, the man's brother's father is also her father — both descriptions land on the exact same person, so the relationship is consistent.

Result: The woman is the man's sister.