1 8 Points Two Languages L L2 Denote Concatenation L L2 Set Strings Obtained Concatenating Q43868304
1. (8 points) For two languages Lị 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. Show transcribed image text 1. (8 points) For two languages Lị 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.
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Answer to 1. (8 points) For two languages Lị and L2, denote their concatenation L L2 as the set of strings obtained by concatena…
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