Classical probability — pairwise independence and a union

Suppose that probabilities are assigned to the subsets of $\Omega=\{a,b,c,d,e,f\}$ according to the classical definition of probability. Which of the following statements is/are true for the sets $A=\{a,b\}$, $B=\{b,d\}$ and $C=\{a,c,d\}$? (I) C and A are independent. (II) C and B are independent. (III) C and $A\cup B$ are independent.