DFA and NFA equivalent language

Question

I'm asked to build a DFA A and NFA B such that L(D) = L(N) with some specific conditions. I'm not asking for solutions or answers; I just wanted to make sure I have the right method to attack this problem.

First off, I'm a bit confused by the wording "build". Do they just want an automaton drawn? Would that be considered "built"?

I'm thinking of drawing the NFA B that fits that condition. Then using the drawing, I'll construct an equivalent DFA A. There's a theorem somewhere that says equivalent automatas have the same language. So I don't have to do anything further to show L(A) = L(B) right?

Thanks!

Answer 1

This sounds about right. Just construct any NFA A that accepts language L(A). Then determinize that NFA to produce DFA B. DFA B should then accept L(A) too. DFA's and NFA's are equivalent in the languages they accept.