P and Q are children of S. Who is the father of P? To answer this question, which of the statements (1) and (2) is/are necessary?
(1) R is the brother of P and the son of T.
(2) U is the mother of Q.

Given: P and Q are children of S. This implies S is either the father or the mother of P and Q. We need to find the specific gender/identity of P's father.
* Let's analyze statement (1): R is the brother of P and the son of T. This tells us that R, P, and Q are siblings. They are children of S and also children of T. Thus, S and T are the parents, but we still don't know who is the father and who is the mother. (Insufficient alone).
* Let's analyze statement (2): U is the mother of Q. Since Q is the child of S, and U is the mother of Q, it implies U and S are spouses, and S must be the male parent (father) of Q and P. (Sufficient alone).

Thus, statement (2) alone is sufficient to establish that S is the father of P.