# What does it mean to take a union of a transition function with a starting state?

$$\delta(q,a) = \begin{cases} \delta_1(q,a) & q \notin F_1 \text{ or } a \neq \lambda \\ \delta_1(q,a) \cup \{q_1\} & q \in F_1 \text{ and } a = \lambda. \end{cases}$$

Look at the second line of the function definition. It's a transition function. $$q_1$$ is the starting state. What does that union mean here? Union of the function range with $$\{q_1\}$$?

The function $$\delta_1$$ is the transition function of an NFA. It outputs a set of states. So $$\delta_1(q,a) \cup \{q_1\}$$ is just the union of two sets of states.