For a database relation $$R(a,b,c,d),$$ where the domains of $$a, b, c, d$$ include only atomic values, only the following functional dependencies and those that can be inferred from them hold:
$$a \to c\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,b \to d$$
This relation is

(a) Consider the relation scheme $$R(A, B, C)$$ with the following functional dependencies:
$$\eqalign{ & A,B \to C \cr & \,\,\,\,\,\,C \to A \cr} $$
Show that the scheme $$R$$ is the Third Normal Form $$(3NF)$$ but not in Boyce-Code Normal Form $$(BCNF).$$

(b) Determine the minimal keys of relation $$R.$$