Please provide the full answer for it!

4. Let X be a language over {0,1}. Define the function ZeroSandwich (X)={0nx0nxX,n0} (a) Show that the class of regular languages is NOT closed under the function ZeroSandwich. (Hint: use the pumping lemma.) (b) Show that the class of non-regular languages is NOT closed under the function ZeroSandwich. (Hint: prove that {02kk0} is a non-regular language using the pumping lemma and use it as a counter-example.)