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  1. L={<M>|L(M) is finite}- undecidable.
  2. $L=\left \{ L\left ( M \right ) |L\left (M\right )=\Sigma ^{*} \right \}$-undecidable
  3. L={<M>|L(M) is recursive}- undecidable.
  4. L={<M>|L(M) is PROPER subset of $\Sigma ^{*}$}- undecidable   [while, L={<M>|L(M) is  subset of $\Sigma ^{*}$}- decidable ]

How these four conclusion is correct? Plz. explain 

in Theory of Computation by (558 points) | 29 views
In original site, you have answers for all these questions... Just search
yes. All are correct. But "why" matters more.
Actually all looks like regular language, but then how undecidable, that part was confusing me. After that I got proof by rices theorem.But I was finding  some more explanation, specially for last one.
Actually their looks were confusing me, that if they are regular or unecidable.

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