Dear Ahmad, your reduction is not fully specified. On input MP, you need to specify your choice of M and M' (as a function of MP).
You write: 'by considering L(MP) = Sigma* ... I do not understand this, MP is provided as input, it could well be that L(MP) is not the language Sigma*.
I strongly recommend that you try to get from your classmates the solution discussed during lecture 36. Anyone who can help please?