Now, Consider one Undecidable problem
ATM = {<M,w>|M is a TM and w is string}
Let R is the given problem.
Now we reduce ATM problem to R'(complement of the given problem).
Let F be the Reduction function for that.
F = "On input M,w "
1. Construct an arbitrary TM M2 which reject all input i.e it accept empty language.
2. Construct TM M1
M1 = "On input <M,w>
a. for each x
b. if(x != w) "reject"
c. if(x==epsilon) "reject"
d. else RUN M on W. if M accept then accept , M reject then reject else loop.
[ M1's language contain either w or nothing ]
3. RUN R TM with input<M1,M2>
4. If R' accept then "accept"
6. If R' reject then "reject"
So, ATM <m R'
==> ATM' <m R
As ATM' is not Turing reconizable language so, R is not Turing reconizable.
[we know ATM is undecidable language but Turing Reconizable language so ATM' is not R.E]
So, the above problem is not R.E.