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: Prove that the following language A is decidable (e.g., give a TM that decides A). A = {⟨M⟩ | M is…

A: We will prove that language A = {⟨M⟩ | M is an NFA and L(M) = B}, where B is a regular language, is…

Q: Problem 4 (Problem 4.21 in the textbook.) Show that the language S is decidable, where S is defined…

A: S={(M)|M is a DFA that accepts w show that language is decidable

Q: language L = {a i b j c k | i 6= j, j 6= k, i 6= k}; it is not a context- free language. Show that…

A: Given : L = {a i b j c k | i == j, j== k, i == k};

Q: NDFA TO DFA 1. Convert the following Non-Deterministic Finite Automata (NFA) to Deterministic Finite…

A: Here, we are asked to convert the NDFA or NFA to equivalent DFA. We will try to find out it's…

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: whether or not L is empty

A: Using the pumping lemma to defined the L is not emply

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

A:

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: 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: e394 Pumping Lemma for Regular Languages Here are three incorrect statements of the Pumping Lemma…

A: Below is the complete solution with explanation in detail for the given questions regarding Pumping…

Q: 1. Given L₁ = {a, abc, a c) and L₂ = {ab, c ba) are the languages over = {a, b, c), determine L₁ L2…

A: Given :

Q: s A ⊆ B if  A = {8, 10, 12, 14}  and  B = {8, 10, 12, 16, 20}?

A: Here,  The elements of set A are { 8, 10, 12, 14 } And the elements of set B are { 8, 10, 12, 16, 20…

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: 2.4: let = {a, b} and the language L = {b a"b a" | n E{1,2,3, ... }}. heck whether the language is…

A: Proved that given language is regular using pumping lemma

Q: 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: 7. Let X be a set of cardinality n > 0. Let E be the set of all subsets of X with even cardinality…

A: Please refer to the explanation below. If you have any clarification please don't hesitate to…

Q: It is well-known that regular languages are closed under the following operations: union,…

A: Finite languages are closed under intersection and complement but not closed under Complement

Q: normalization, and strong normalization to explain how many normal forms the term ten has, and if…

A: The lambda-term "ten" is defined as "take 10 [0, 1, 2, ...]" which corresponds to the Haskell…

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: Build a PM that accepts the language of all words that have an a as the middle letter: (These words…

A: 1)The Language that accepts all the words that have an a as the middle letter is: waw' where w and…

Q: Please classify the following languages as 1. in P         2. In P but not in NP         3.…

A: Hi there, Please find your solution below, I hope you would find my solution useful and helpful.…

Q: Question 7: Prove the non-regularity of the given language L using pumping lemma. L={a"b?na2n}

A: Pumping lemma: Pumping lemma is used to prove non regularity of the language. The regular language…

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: Problem 1: Considering the alphabet E (a,b} derive a Non-Deterministic-Finite Automaton (NFA) using…

A: Given regular expression is b*ab|bab*. The regular expression defines the language with strings…

Q: 8. H= { (01)™ 2™ | m >0 }

A: Proved the given language nonregular using the pumping lemma

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: Q2. Determine whether each of these statements is true or false. x ∈ {x} {x} ⊆ {x} {x} ∈ {x} ∅…

A: Here is the answer to each of these statements whether true or false with an Explanation.

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: (a)  Give the definition of an isomorphism from a graph G to a graph H. (b)  Consider the graphs G…

A: Two graphs are said to isomorphic if they contains same number of vertices that are connected in the…

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: No need to apply pumping lemma in this Queshon Demonstrate or that ; prove L= {w e {a,b,c,d}*…

A:

Q: 5. A set of formulas Mo is an axiom system for a set of formulas M if {A A is a model for Mo} = {A |…

A: Answer is explained below in detail

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: Problem 2-6. Regular Languages Prove the following languages are regular languages: Sipser, Exercise…

A:

Q: 2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r€ RB, let L(r) be the…

A: Regular Expressions Just as finite automata are used to recognize patterns of strings, regular…

Q: 7. G ={ 1ky | and y E { 0, 1 }* }

A: Proved the given language is nonregular