# ε-NFA to DFA - initial state with only epsilon transitions

I am having trouble discovering how to convert a ε-NFA to DFA (image below) when all transitions in the initial state are epsilon transitions. I already know how to convert ε-NFA to DFA (common cases), but this case I never saw before.

Thank you guys!

Here is an algorithm to convert an $$\epsilon$$-NFA to an equivalent DFA.
Let the $$\epsilon$$-NFA consist of a set of states $$Q$$, an initial state $$q_0$$, a set of accepting states $$F$$, and a transition function. We construct a DFA on the set of states $$2^Q$$ (the power set of $$Q$$). The initial state is the $$\epsilon$$-closure of $$q_0$$ (the set of all states in $$Q$$ reachable from $$q_0$$ by a path of $$\epsilon$$-transitions). A state is accepting if it intersects $$F$$. We define the transition function $$\delta$$ as follows: given a state $$S \in 2^Q$$ and a letter $$a$$, $$\delta(S,a)$$ consists of all states in $$Q$$ reachable from a state in $$S$$ by taking an $$a$$-transition followed by a path of $$\epsilon$$-transitions.