Random Trivia Give a brief, concise answer for each of the following questions. If it asks for a proof, you don't have to do a formal research paper proof, but there should be a clear sequence logic. (a) For what languages (L) is L* finite? . (b) Describe two languages, A and B, where such that |A · B| < |A| · |B| (c) Prove (AUB)* = (A* B*)* for all languages A and B.

I need help solving 1 and 2

Is the language composed of all strings over the alphabet {a,b} that contain an odd number of a's a regular language? If so, show why. Note, again, that you may use any line of argument on regular languages, e.g., by drawing the FSA,or by using Closure properties of regular languages, along with the fact that the language is regular

2. Consider the FUN language, prove the following expression evaluates to 3 with respect to the big-step operational semantics that can handle recursion. let z = 2 in z+1