I am recently learning about automaton and I was confused at an exercise that was given to me.In the lecture, we were given this exercise:Given a FA with transitions $$\begin{array}{c|ccc}    &      a       &      b      & \epsilon \\ \hlineq_1 & \varnothing  & \varnothing & \{q_2\} \\q_2 & \{q_3, q_4\} & \varnothing & \varnothing \\q_3 & \varnothing  & \{q_4\}     & \{q_2\} \\q_4 & \{q_5\}      & \varnothing & \{q_3,q_5\} \\q_5 & \varnothing  & \varnothing & \varnothing\end{array}$$With $E(\{q_1\}) = \{q_1, q_2\},E(\{q_2\}) = \{q_2\},E(\{q_3\}) = \{q_2, q_3\},E(\{q_4\}) = \{q_2, q_3,q_4, q_5\},$ how do you construct something as $E(\{q_1, q_3, q_5\}) = \{q_1, q_2, q_3, q_5\}$?
Constructing Epsilon-closures
automata;finite automata