Understanding how to decide whether a language for a DFA is decidable So from what I understand, if a language is recognisable then using a TM it can be accepted and halted or rejected or halted, however a language that is decidable can be accepted and always halts on rejection?

Given the language $A_{\mathrm{DFA}} = \{\langle A \rangle\mid A \text{ is a DFA and } L(A) = \{0, 1\}^∗\}$ , I want to determine if it is decidable.

What I have come up with so far is that it is a recognisable language, I don't believe it can be rejected, only accepted and halted due to the fact once the read head comes across a blank it can just accept it.  Is this the way I should be thinking?  Am I correct in thinking it is not decidable or is this not a valid way to argue the point?

What should my process of thinking be when I am trying to prove it by contradiction if it is not decidable?

Thanks in advance for any tips!
Let me rephrase the question:


  Is there an algorithm that, given a DFA, decides whether its language is $\{0,1\}^*$?


Such algorithms do exist, hence the corresponding set is decidable.

I'm not sure what your instructor means by "high level description of a Turing machine", but what they should have meant is "describe an algorithm that solves the problem". Hopefully you already know how to do that.