Pointing to a woman, a girl says, 'She is the mother of the only child of my father-in-law.' How is the woman related to the girl?

Introduction / Context:
This problem combines marital relations with the concept of father-in-law and only child. A girl points to a woman and describes her as the mother of the only child of my father-in-law. Your job is to determine how that woman is related to the girl. The puzzle checks whether you can correctly interpret who the only child is and then identify that child's mother.

Given Data / Assumptions:
- Speaker: a married girl. - She has a father-in-law, that is, her husband's father. - The father-in-law has exactly one child (the only child). - The woman being pointed at is the mother of this only child. - Standard monogamous family structure is assumed.

Concept / Approach:
The father-in-law is the girl's husband's father. If he has only one child, that only child must be the girl's husband. The mother of the husband is the girl's mother-in-law. Therefore, the woman being pointed at is the girl's mother-in-law. The key is to correctly identify that the only child of my father-in-law is not the girl herself but her husband.

Step-by-Step Solution:
Step 1: Interpret my father-in-law as the father of the girl's husband. Step 2: The phrase only child of my father-in-law means that this man has exactly one child. Step 3: Since father-in-law is the husband's father, this only child is naturally the husband of the girl. Step 4: The woman being pointed at is described as the mother of this only child. Thus she is the mother of the girl's husband. Step 5: The mother of one's husband is, by definition, the mother-in-law. Step 6: Therefore, the woman is the girl's mother-in-law.

Verification / Alternative check:
Draw a small tree: place the father-in-law and the woman (his wife) at the top as a couple. They have exactly one child, the husband. On the next level, the husband is married to the girl. From the girl's perspective, her husband's parents are her father-in-law and mother-in-law. The wording that the woman is the mother of the only child of my father-in-law fits perfectly when the child is her husband, confirming that the woman is the girl's mother-in-law.

Why Other Options Are Wrong:
- Granddaughter: This would mean the girl is two generations below the woman, which is not indicated. - Mother: The girl's own mother is not described; the woman is explicitly related through the father-in-law. - Cousin: Cousins are usually from the same generation and do not arise directly from father-in-law relationships. - Sister-in-law: A sister-in-law would be the sister of the husband or the wife of a brother, not the husband's mother.

Common Pitfalls:
A common mistake is to think that the only child might be the girl herself, but the father-in-law is defined via the husband, not directly via the girl. Another pitfall is to mix up mother-in-law and grandmother-in-law when multiple generations are mentioned. Here only two generations are involved above the girl, making the relationship clearly mother-in-law. Careful reading of whose father and whose child is being discussed keeps the logic straight.

Final Answer:
The woman pointed to by the girl is her mother-in-law.