In a family, I. A is the father of B. II. C is the son of A. III. D is the brother of E. IV. E is the…

The correct choice is: “Uncle”

From I and II, B and C are both children of A, so C is B's brother.

From III and IV, E is B's daughter and D is E's brother, so D is B's son.

C is therefore the brother of D's parent, B. The brother of one's parent is one's uncle, so C is D's uncle.

C and D are in different generations, so C cannot be D's “Brother” or “Cousin”; and “Nephew” reverses the relationship (D is C's nephew).