The correct answer is: C. Either (1) or (2).
Statement (1) tells us that C is the brother of A and the son of E. This means that A and C have the same father, E. However, it does not tell us whether A’s father is also B’s father. Statement (2) tells us that F is the mother of B. This means that B has a mother, F. However, it does not tell us whether B’s father is also A’s father.
In order to determine whether A’s father is also B’s father, we need more information. Either statement (1) or statement (2) is necessary, but neither statement is sufficient.