1. (8 points) For two languages L and L2, denote their concatenation L L2 as the set of strings obtained by concatenating strings from each of the languages: LiL2 = {xy | X E L1,Y E L2}. Prove (via a formal proof using set-theoretic axioms) or disprove (via a counter-example) that: (a) (4 points) If L1, L2, L3 are languages, and L2 C L3 then L L2 CL L3. (b) (4 points) If L1, L2 and L3 are languages, then L1 (L2 N L3) = L; L2 NL/L3