recursive or recursively enummerable

Question

State whether these languages are recursive ,RE, non RE?

L1 = {<M>| M is a TM and |L(M)| ≤ 3}.

L2 = {<M>|M is a TM and |L(M)| ≥ 3}.

Answer 1

By Rice Theorem 

For L2, we can have T_yes = Σ^* and T_{no =} Ф but here we cannot have Tyes and Tno such that L(Tyes)⊂L(Tno). So L2 is not recursive.

For L1, we can have T_no = Σ^* and T_{yes =} Ф and here L(Tyes)⊂L(Tno) So L1 is not RE.

Comments

hey, Gate Mission 1 can you please explain it further