Let N = ( {}, Q, , q0, {qf }) be a NFA and let L = L(N) be the language accepted by N. For N assume q0 has no incoming transitions and qf has no outgoing transitions. For each of the following FAs that are modifications of N describe the language accepted by each in terms of L.

(a) A -transition is added from qf to q0.

(b) Add a -transition from q0 to every state reachable from q0 along a path with labels that may be or symbols from .

(c) Add a -transition to qf from every state that reach qf along some path.

(d) The FA where both (b) and (c) are done.