Can anyone help me to prove that the following language is nod decidable?
$$ A=\{\langle\,M,w,q\,\rangle\mid M \text{ is a $TM$ , $w$ is a word, $q$ is a state in $M$ and while $M$ runs on $w$ it visits the state $q$}\}$$
I can use rice theorem and reductions.
My intuition is that A is not decidable and I think we should prove it by assuming in contradiction that $A\in R$, hence there is $TM$ $S$ that decides $A$ and we can use it to build $TM$ $T$ that decides $A_{TM}$. contradiction to the fuct that $A_{TM}\notin R$.
any help will be apriciated!