We know that C is a connected subset of X, iff C is connected in the subspace topology. Therefore, from the definition of subspace topology, we know that there should be a V subset of C, and there should exist an open set U that belong to the topology, s.t. $V = $U $\cap$ C$.
Also, $C \subset D \subset$ $C^{bar}$, from here we can say that one of them in dense in D, I think it will be C bar. Then, i need to show that there doesn't exist a separation of D, i.e. there doesnt exist non empty sets U and V in D. I am having a hard time figuring how to relate those and show D is connected or not separated.
Can someone help me here?
