To solve this logical reasoning problem, let's break down the relationships and find out how A is related to B.
- A says to B, "I am the mother of your grandfather's son."
- Let's analyze "your grandfather's son":
- "Your" refers to B.
- "Grandfather's" refers to B's grandfather.
- "Grandfather's son" would be B's father, assuming here that the grandfather has a son and not a daughter who could be another parent figure.
- Therefore, "the mother of your grandfather's son" translates to "the mother of B's father."
- The mother of one's father is one's grandmother.
Thus, A is B's grandmother.
Now, let's examine why the other options are incorrect:
- Sister: A cannot be B's sister because B's sister would not fit the description of being the "mother of your grandfather's son."
- Daughter: A cannot be B's daughter because the daughter would be a child of B.
- Grandson: A cannot be B's grandson because the grandson refers to a male descendent of B, while A is described as a mother.
Therefore, the correct answer is Grandmother.