Condition (1) ⇒ A * B = A is the father of B. So Y * Z = Y is Z’s father. Y is father. Condition (2) ⇒ A $ B = A is the son of B So X $ Y = X is the son of Y. X and Z is brother. Condition (3) ⇒A # B = A is the sister of B. Hence Z # W. = Z is the sister of W. So X is the brother of W.