Symbolic family code: ‘P $ Q’ = P is brother of Q; ‘P # Q’ = P is mother of Q; ‘P * Q’ = P is daughter of Q. In “A # B $ C * D”, who is the father?

Introduction / Context:We must decode a compact kinship expression with three operators and identify which person must be the father in the family described.

Given Data / Assumptions:

• $ → brother of; # → mother of; * → daughter of.
• Expression: A # B $ C * D.

Concept / Approach:Expand the relations: A is mother of B; B is brother of C; C is daughter of D. From this, deduce parentage and identify the father.

Step-by-Step Solution:1) A # B → A is mother of B.2) B $ C → B is brother of C → B and C share at least one parent; A is mother of B ⇒ A is also mother of C (standard MCQ assumption).3) C * D → C is daughter of D → D is a parent of C (gender not specified yet by this operator alone).4) Since A is explicitly the mother, the other parent D must be the father.

Verification / Alternative check:“Brother of” only constrains gender and siblinghood, not parentage direction beyond sharing a parent with C—consistent with A as mother and D as the remaining parent (father).

Why Other Options Are Wrong:B and C do not have parent roles here; “Data inadequate” is incorrect because the father is uniquely identifiable.

Common Pitfalls:Assuming “daughter of D” means D is necessarily mother; it only signals parentage, and with A fixed as mother, D becomes father by elimination.

Final Answer:D