C -> D is preserved in the first relation, D -> E in the second one.

Now when we want to check if C -> DE is preserved, we consider the union of the FDs obtained from the decomposed relations and then try whether we are able to get what we need or not. So in this case, we have C -> D and D -> E with us.

When we take closure of C, we get C -> CDE, and thus, we are able to get C - > DE in this decomposition.