well I'm kind-of stuck on this question:

Let ALL DFA = { <A> | A is a DFA that recognizes ∑* }. Show that ALL DFA is decidable.

I have to prove this two different ways. So far I figured out one, and can't think of any other way...any ideas?

here is the first solution:

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ALL DFA == E DFA, we know that E DFA is decidable (theorem 4.4) and since decidable languages are closed under the comlpement operation, ALL DFA is decidable.