decidablity

Question

M is a TM ,language accepted by L(M) is regular is not recursive enumerable? why?

Answer 1

L= {TM | TM accepts regular}

Here we want in output all those TM's which are accepting only regular languages. But since we are just given a TM in input, looking at a TM we cannot say whether it will accept ONLY regular. It may accepts CFLs or Recursive language also, so we need to run and see over infinite strings whether the TM which we have is accepting only Regular.

Hence its not recursively enumerable