Theory of Computing - thank you so much!

3. Finite and cofinite. Let ={a,b}. Define FINITE to be the set of all finite languages over , and let coFINITE={LLFINITE} (where, for any language L over ,L is the complement of L, that is, \L ). For example, is in coFINITE because its complement is , which is finite. 2 (Please think carefully about this definition, and note that coFINITE isn't the same thing as FINITE.) (a) Are there any languages over in FINITE coFINITE? Prove your answer. (b) Are there any languages over that are not in FINITE coFINITE? Prove your