Suppose f : A → B and g: B C. (a) Prove that if f is surjective and g is not injective, gof is not injective. (b) Prove that if f is not surjective and g is injective, go f is not surjective.

Q: Let W = { ⟨X,Y⟩ | X and Y are DFAs and L(X) ⊆ L(Y)}. Show that W is decidable.

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Q: Use a direct proof technique to prove the following theorems:   For all integers x and y, x2 + y2 −…

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Q: Prove that the language {a*b"a" | k20, n20} is not regular. Do not use pumping lemma!

A: Here, we have to prove that given language {akbnan | k>=0, n>=0 } is not regular language…

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Q: Using Pumping Lemma, Prove whether the given language is Regular or not. {w|w € Even Palindrome}

A: Given language regular or not defined by pumping lemma

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

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Q: 1. Is the following language A regular or non-regular? A = {1" 0m 1" | 0 ≤ m, n ≤ 3 and m=n+2} 2. If…

A: The above language A has following conditions. 0≤m,n≤3   and   m=n+2 So one possibility is , n=0 and…

Q: 1. Using pumping lemma prove that the following language L is non-regular. L = {an²in>0}

A: Answer the above question are as follows

Q: 1. Show that the language of even strings over (0,1) that begin and end with 0 is regular. Give both…

A: The Answer is

Q: 3. Consider the languages L= { ba" a b" | n > 0 } a.) Use the Pumping Lemma for Regular Languages to…

A: According to the Bartelby guidelines we are suppose to answer one question at a time. Kindly repost…

Q: G= ({S, A, B, C}, {a,b,c}, S, P) where P S → AB A AB|CB| a BAB b CAC C

A: NPDA stands for non-deterministic pushdown automaton. It is basically a type of computational model…

Q: 1. Is the following set of connectives functionally complete? Explain. {→, 1}

A: Given: The truth function are {0,1} {→,⊥}

Q: (1) State the pumping lemma with all its conditions and indicate how you go about proving that a…

A: the pumping lemma with all its conditions and indicate  you go about proving that a language is not…

Q: Suppose we augment PC with an exclusive or binary operator, ⊕. Modify the model theoretic semantics…

A: XOR operation XOR is one of the sixteen possible binary operations on Boolean operands. That means…

Q: QUESTION 1 Let an automaton A1 be given by the following diagram: a a b 90 92 93 Find a minimal…

A: Defined the minimal deterministic automaton for the given automaton

Q: K. Reversal & Homomorphism Let E = (10)* + (01)* h(0) = ab h(1)= ba 1. ER = ((10)* + (01)*)R = union…

A: Answer:)

Q: Use the pumping lemma to prove that the language L over {a,b,c}", given by L = {wcv: |wa = |vl6} is…

A: First lets see Pumping lemma for regular languages: If a language L is regular, then there exist an…

Q: ) If the languages are regular, give an automaton. Otherwise, show it is not regular by using…

A: To show that L = {b^2 a^n b^m a^3 | m, n ≥ 0} is a regular language, we need to construct a finite…

Q: The alphabet of the language is (a, b, c): Use pumping lemma to prove that the language (abc n>0} is…

A: Given grammar:

Q: ose that L is a language on a

A: Say a group of languages is closed under an operation if the outcome of applying the operation to…

Q: P is the class of language that are decidable in polynomial time

A: ANSWER : Union: Let Li (i = 1, 2) be two languages in P and let Mi be a DTM that accepts Li in…

Q: Given A and B are sets, prove that (A ⋃ B) ⋃ C = A ⋃ (B ⋃ C) by showing (A ⋃ B) ⋃ C ⊆ A ⋃ (B ⋃ C)…

A: We are going to prove associative property in sets which is : (A ⋃ B) ⋃ C = A ⋃ (B ⋃ C). Please…

Q: L= {a"bn+1}

A: Since you are asking multiple questions, we are answering first question for you. If you want…

Q: Given functions f:R → R and g: R → R. Suppose that go f turns out as go f(x) = (x2 + 7]. Identify…

A: f:R→R f(x)=x2+2 g:R→R g(x)=x−1x​ fog(x)=f(g(x)) =f(x−1x​) =(x−1x​)2+2 =x2−2x+1x2​+2…

Q: Q.4: let E= {a, b} and the language L = {b a"b a" |nE{1,2,3,... }}. Check whether the language is…

A: The Answer is in Below Steps

Q: Could you lend a hand with this issue? I'm struggling with it, and it would be immensely helpful if…

A: Explained in the answer only

Q: Problem 1. the regular expression a* bc* d. Consider the language of strings over the alphabet…

A: 1. Thompson's construction method: The regular expression a* bc* d can be represented by the…

Q: Show that if a language family is closed under union and complementation, it must also be closed…

A: Hello student Greetings Hope you are doing great. Thank You!!!

Q: L= { am bn | m < n} This language is/isn't Regular? Prove it using with Pumping Lemma.

A: L=am bn | m&lt;n is not regular. Let us assume to the contrary that Language L is regular.

Q: 1. Is the following language A regular or non-regular? A = {1" 0 1" |0 ≤m, n ≤ 3 and m = n + 2} 2.…

A:

Q: Question 2 1. Let L by a language over E. For each of the following statements about L, determine…

A: According to our guidelines we solve only first one: ================================== about…

Q: State the pumping lemma with all its conditions and indicate how you go about proving that a…

A: State Рumрing  Lemmа  is  used  аs  а  рrооf  fоr  irregulаrity  оf  а  lаnguаge.  Thus,  if  а…

Q: A= B if and only if : * A is subset from B and B is not subset from A A is not subset from B and B…

A: Find the answer with explanation given as below :

Q: 2. Exhibit an enumeration to show that the set of all tuples (of any finite length) of nonnegative…

A: Step 1 A set S is countable if there is a bijection f:N→S. An infinite set for which there is no…

Q: For languages A and B, let the shuffle of A and B be the language {w/w = aibi akbk, where a₁ ak E A…

A: A regular language is a type of formal language that can be described using regular expressions,…

Q: What does the Pumping lemma for regular languages say?

A: Explanation:   Pumping lemma is used to prove a given language is non-regular. It doesn't prove that…

Q: Deterministic Finite Acceptors (DFAs) For = {a,b), construct a DFA that accepts the set consisting…

A: DFA stands for Deterministic Finite Automata.It is  a  finite state machines that accept or reject…

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