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.