The following statements are made based on the relationships given above. (1) R is the grandmother of S. (2) P is the uncle of S and T. (3) R has only one son. (4) Q has only one daughter. Which one of the following options is correct?

From the given relationships, we can determine the family structure:

1. $\text{R}$ is female (mother of $\text{Q}$).

2. $\text{P}$ is male (brother of $\text{Q}$). Thus, $\text{P}$ is also a child (son) of $\text{R}$.

3. $\text{Q}$ is the parent of $\text{S}$ and $\text{T}$, but the gender of $\text{Q}$ is not specified.

4. $\text{S}$ is female (daughter of $\text{Q}$).

5. $\text{T}$ is female (sister of $\text{S}$, hence also a daughter of $\text{Q}$).

Now evaluating the statements:

• Statement (1): Since $\text{R}$ is the mother of $\text{Q}$ and $\text{Q}$ is the parent of $\text{S}$, $\text{R}$ is the grandmother of $\text{S}$. (True)

• Statement (2): Since $\text{P}$ is the brother of $\text{Q}$ (parent of $\text{S}$ and $\text{T}$), $\text{P}$ is the uncle of both $\text{S}$ and $\text{T}$. (True)

• Statement (3): The gender of $\text{Q}$ is unknown (could be male or female), so we cannot conclude that $\text{R}$ has only one son. (False / Not definitely true)

• Statement (4): Both $\text{S}$ and $\text{T}$ are daughters of $\text{Q}$, meaning $\text{Q}$ has at least two daughters. (False)

Therefore, Both (1) and (2) are true, which corresponds to option (A).