$5\mathrm{.}28$ Rice$$s theorem. Let P be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given Turing machine$$s language has property P is undecidable. In more formal terms, let P be a language consisting of Turing machine descriptions where P fulfills two conditions. First, P is nontrivial$$it contains some, but not all, TM descriptions. Second, P is a property of the TM$$s language$$whenever L$($M$1)=$ L$($M$2),$ we have $$M$1$ in P iff $$M$2$ in P$.$ Here, M$1$ and M$2$ are any TMs$.$ Prove that P is an undecidable language. $5\mathrm{.}29$ Show that both conditions in Problem $5\mathrm{.}28$ are necessary for proving that P is undecidable.