Independence Is Not Transitive

Let $\Omega = \{1,2,3,4\}$ with uniform probability. Define $A = \{1,2\}$, $B = \{1,3\}$, $C = \{3,4\}$. (a) Verify that $A$ and $B$ are independent. (b) Verify that $B$ and $C$ are independent. (c) Are $A$ and $C$ independent? What does this say about transitivity of independence?