Question: Given a nonempty language A*, prove that if A2 = A, then A.

Given a nonempty language A⊂∑*, prove that if A2 = A, then λ ∈ A.

Step by Step Solution

★★★★★

3.38 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let E be an alphabet with A If A 1 and x A then xx x since A 2 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

954-M-L-A-L-S (7776).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Define the distance between two nonempty subsets A and B of R" by a) Prove that if A and B are compact sets which satisfy A B = , then dist(A, B) > 0. b) Show that there exist nonempty, closed sets...

Q:

Let S R be nonempty. Prove that if a number u in R has the properties: (i) for every n N the number u - 1/n is not an upper bound of S, and (ii) for every number n N the number u + 1/n is an upper...

Q:

Let E be a set in Rm. For each u: E R which has second-order partial derivatives on E, Laplace's equation is defined by a) Show that if u is C2 on E, then Îu = (u) on E. b) Show that if E R3...

Q:

Problem 1 [3 points) Let A, B be regular languages over alphabet E. Is the following language regular? Prove your answer. A2 = {x|x A, R&B} Problem 2 [3 points) Let C be a language defined over...

Q:

Given the following language: { a n b m a n b m } . Prove whether it is regular or nonregular. If regular, show FA . If nonregular, prove using the pumping lemma by showing how many partitions are...

Q:

Given any regular language L, prove that its reversal LR is also regular (LR = WR | WEL). In other words, if L is accepted by a DFA M then its reverse is also accepted by another finite automaton...

Q:

1 [10 POINTS] COUNTABILITY OF POLYNOMIALS Show that the set of all polynomials in the single variable x with integer coefficient is count able. Such polynomials are of the form aixi, for some natural...

Q:

2. (7 points) Common Pumping Lemma Misunderstandings (a) (2 points) You are a CS4510 TA, and you are grading the following question: "Is the language L = {w w is a binary string with at least as many...

Q:

Please prove a) and b) parts of the question. Thank you! Let L be a non-empty language. Show that L C L2 if and only if e E L. That is, prove both a) Let L is a non-empty language. If e E L, then L C...

Q:

Hello I have an automata homework could you help me? Prove or disprove each of the following assertions: [1 Points]Every nonempty language contains a nonempty regular language. [1 Points]Every...

Q:

A uniform cube of side length 8.0 cm rests on a horizontal floor. The coefficient of static friction between cube and floor is . A horizontal pull P is applied perpendicular to one of the vertical...

Q:

A barometer can be used to measure an airplane's altitude by comparing the barometric pressure at a given flying altitude to that on the ground. Determine an airplane's altitude if the pilot measures...

Q:

3 Green Corporation, a calendar year taxpayer, has ordinary income of $10,000 and a long-term capital loss of $12,000 in 2017. For past years, it had a longterm capital gain of $2,500 in 2014 and a...

Q:

In June 2013, Microsoft announced that its new Xbox One video game console would have a price of $499. Sony then announced that its new PlayStation 4 video game console would have a price of $399. An...

Q:

David is driving on the highway at the legal speed limit of 70 mi/h. He notices that there is an accident up ahead approximately 200 feet away. His reaction time is approximately 3 / 4 of a second....

Q:

Martine is driving on an interstate at 70 km/h. She sees a traffic jam about 50 meters ahead and needs to bring her car to a complete stop before she reaches that point. Her reaction time is...

Q:

Model the total stopping distance by the equation y = x2 / 20 + x, where 20 x represents the speed in miles per hour and y represents the total stopping distance in feet. a. Graph this equation for...

Q:

the following table: (Note: Assume a 365-day year.) a. Calculate the approximate cost of giving up the cash discount from each supplier. a. The approximate cost of giving up the cash discount from...

Q:

Route Canal Shipping Company has the following schedule for aging of accounts receivable: a. Calculate the percentage of amount due for each month. b. If the firm had $1,716,000 in credit sales over...

Q:

P3-6 (Algo) Analyzing the Effects of Transactions Using T-Accounts, Preparing an Income Statement, and Evaluating the Net Profit Margin Ratio LO3-4, 3-5, 3-6 [The following information applies to the...