Concept:
Blood relation questions require careful interpretation of family relationships described in a statement. The best approach is to simplify the statement step-by-step and identify each relationship logically.
Step 1: Start with the innermost part of the sentence.
The statement says:
\[
\text{"my father's only son"}
\]
Since the boy himself is speaking, the phrase
"my father's only son" refers to
the boy himself.
Step 2: Identify the next relation.
The sentence now becomes:
\[
\text{"the mother of my father's only son"}
\]
Since the father's only son is the boy, the
mother of the boy is simply
his mother.
Step 3: Interpret the complete statement.
The girl is described as:
\[
\text{"the daughter of my mother"}
\]
The daughter of the boy's mother would be:
- Either the boy himself (if he were a girl) or
- His sister
Since the statement refers to a girl, the relationship must be:
\[
Sister
\]
Step 4: Final answer.
\[
\boxed{\text{Sister}}
\]