Question $3$:

Halt when started on blank tape. Consider the language

$HAL{T}_{}=\{($:$M$:$)|M$ halts $on$ input $\}$

Can Rice's theorem be used to directly show that $HAL{T}_{}$ is undecidable?

$($a$)$ Suppose you try to use Rice's Theorem. What property $P(M)$ of Turing machines $M$ would be relevant here?

$($b$)$ Is this property trivial? Explain why it is$,$ or prove that it is not.

$($c$)$ Is this a property of languages? Explain why it is$,$ or prove that it is not.