# problem with the NFA to DFA conversion theorem

I have been given the following NFA:

and, using the conversion algorithm (creating a new event for every union of events), I came up with the following DFA (note: I added here the events from the NFA, even if they are never accessed, for clarity on how the union events are formed):

However, I can clearly see that something is wrong: the NFA rejects the string "ababa", yet my DFA accepts it. The transition $\delta^*(\{A,C,D\},a)$ returns the event $\{A,B,D\}$, an accepting state. Through sheer intuition, I imagine it should instead return the event $\{A,B\}$, but I don't quite see what went wrong. I've redone this multiple times, each time with the same result. What I am doing wrong in my application of the theorem?