In this problem you will prove that -transitions are merely syntactic sugar that makes writing NFAs easier, but -transitions are not necessary, not even to help reduce the number of states needed.

Prove that for every NFA N = (Q,,,s,F), there is an NFA N = (Q,,,s,F) with no -transitions such that L(N) = L(N). Note that N should have the same state set as N.