8. Let Σ; be alphabets for i = 1, 2, 3, and L; C Σ;, i = 1, 2, 3 be three languages. Prove that (a) L₁ (L2 UL3) = L₁ L2 UL1L3. (b) (L₁L2) L3 ‡ L1L3NL2L3, in general. (c) L₁ (L2 − L3) ‡ L₁L2 – L₁L3, in general. (d) (L₁UL₂)* = (L1L₂)*.

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Q: L+Ø, and L2022 L2023 and Lº + L - your answer. hat for every non-empty language L over an alphabet…

A:

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A: Proved that given language is not regular

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Q: Let A1, A2, and A3 be languages defined over an alphabet Σ. Define Majority(A1, A2, A3) = {w | w is…

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A: Below i have provided handwritten solution of the problem. See below steps.

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A: Introduction:

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A: Given :  Given the language L(r) defined over the alphabet Σ = {a,b}, where r = (0011)*

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A: please check the step 2 for solution

Q: Given a language L over the alphabet Σ, define f(L) = {vo : v € L,o € Σ, and v=uo for some u € [*}

A: Note : A language is said to be regular iff it is accepted by a Finite Automata. Given a language L…

Q: Create a complex CFG that produces L. s L = {0¹ 14 | i≥ 0}. Prove the ambiguity and construct a PDA…

A: Below i have given handwritten solution of the problem. see below steps.

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A: Below is the answer to above question. I hope this will be helpful for you..

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A: We need to prove the set of all languages over sigma is uncountable.

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A: The complete solution is below:

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A:

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A: Note As Per over guidelines we will solve three sub part remaining sub part post separately i did 2…

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A:

Q: Prove that the language {1®0"1k |k> 0, n > 0} is not regular. DO NOT use pumping lemma.

A: Closure Property of regular language: Regular languages are closed under concatenation. It means…

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A: Given that:

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A: Please upvote Please. I am providing you the correct answer please upvote please. I need it badly.…

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A: Answer:    the language consists of strings which has the number of 0's is twice the number of 1's.…

Q: Show that if L is a cfl, then Suffix(L) = {v : uv ∈ L} is also a cfl.

A: . Show that if L is a cfl, then Suffix(L) = {v : uv ∈ L} is also a cfl.

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A: The answer is

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A: Below is the answer to above question. I hope this will meet your requirement

Q: Let L be the language L-{anbmc2n | (n+2n)>m) over the alphabet Σ=(a,b,c). Prove that L is not…

A:

Q: 8. Let Σ; be alphabets for i = 1, 2, 3, and L, Σ, i = 1, 2, 3 be three languages. Prove that (a) L₁…

A:

Q: Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF {wct | t ∈…

A: The Answer is in step2