For two languages L and L2, denote their concatenation L L2 as the set of strings...

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For two languages L₁ and L2, denote their concatenation L₁ L2 as the set of strings obtained by concatenating strings from each of the languages: L₁ L₂ = {xy | x E L₁, y = 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 L₁ L2 C L₁L3. (b) (4 points) If L₁, L2 and L3 are languages, then L₁ (L₂L3) = L1 L2 NL1L3. For two languages L₁ and L2, denote their concatenation L₁ L2 as the set of strings obtained by concatenating strings from each of the languages: L₁ L₂ = {xy | x E L₁, y = 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 L₁ L2 C L₁L3. (b) (4 points) If L₁, L2 and L3 are languages, then L₁ (L₂L3) = L1 L2 NL1L3.

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a Let x and y be strings from L1 and 42 respectively Since L2 C L3 we must have ... View the full answer