Lilly and Michael are studying abstract algebra and are working on a problem involving group theory. They are given the following set: S = {1, 2, 3, 4, 5, 6} and the binary operation * defined as follows:
a*b = (a+b) mod 6
They are asked to determine whether the set, S, with the operation * forms a group.

They must first check that the operation * is closed for all a and b in S, meaning that when they perform the operation on any two elements in S, the result is also in S.
They must check that the operation * is associative, meaning that (ab)c = a(bc) for all a, b and c in S.
They must check that there is an identity element in S, meaning that there is an element e in S such that a*e = a for all a in S.
They must check that for every element a in S, there is an inverse element a^-1 in S such that a*a^-1 = e.
Lilly and Michael will have to work through these steps to determine if the set S with operation * forms a group or not.

Answers

Answer 1

The thing that should be fine regarding the algebra is A. They must first check that the operation * is closed for all a and b in S, meaning that when they perform the operation on any two elements in S, the result is also in S.

What should they do first?

They will need to check that the operation * is closed, associative, has an identity element, and that every element has an inverse in order to determine if the set S with operation * forms a group.

They can check each of these conditions by working through examples and verifying that they hold for all elements in S. If the set S with operation * satisfies all of these conditions, then it is a group. If it does not satisfy one or more of these conditions, then it is not a group.

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Related Questions

give an example of a time you have had to deal with change, professionally or personally?

Answers

Professionally: dealing with a change of a co worker and having to readjust
Personally: Moving and having to switch schools and make new friends

Is it better to write in MLA or APA format? And why

Answers

Answer:

MLA is more commonly used than APA at the high school level. ... MLA (Modern Language Association) format is used for humanities and literature works. APA (American Psychological Association) is used for technical and scientific works. Each writing style is formatted to make citations for that specific field easier

Explanation:

Please select the word from the list that best fits the definition

Shows boundaries of cities

Answers

Answer:

Political Maps

Explanation:

Please select the word from the list that best fits the definition

Shows boundaries of cities

Answer:

Political Maps

Explanation:

When might it be most helpful to clear your browser's cache of temporary Internet files?

Answers

Answer:

when you look at errotic videos

Explanation:

really?

It’s a good idea to clear it every few weeks.

O tema do texto e
(A) O calor intenso que faz sobretudo nos esta
dos brasileiros da regido
(B) O risco à saúde pe
nutenção adequ
Um novo ar-con
desenvolvido para
0) A vasta fauna de fun
bita os dutos do ar-cond​

Answers

Answer:

Explanation:

uiljlrdfhgj';l;kfjhk,./

What issues may arise if nominal gross domestic product was used instead of real gross domestic product?

Answers

Answer: See explanation

Explanation:

Real gross domestic product is simply refered to the economic output of a particular country which has been adjusted for price changes as inflation was taken into consideration.

Nominal gross domestic product is the measurement of the gross domestic product of a particular country which makes use of current prices, and isn't inflation adjusted.

The issue that may arise when nominal gross domestic product was used instead of real gross domestic product is that the nominal GDP leads to the inflation of the growth figure in the economy. This is because the nominal GDP doesn't take inflation into effect.

This leads to the misleading of the GDP since there'll be an overstatement of the GDP even though it was actually a rise in the inflation rate for the particular economy.

Caculate the difference between the greatest and least landing values.

Answers

Answer:

ghjkiikjhhllnvgtullnvg

Answer:

where is the question?

plz make it in right way

Students have to pay to go to
4 points
kindergarten
high school
middle school
private school
Other:

Answers

Students have to pay to go to college, so I would say other. Although, parents do have to pay for their kids to go to private school. Hope this helps!

Mr. Martinez praises Nolan in front of the rest of the class for raising his hand and answering a discussion question correctly. The next day during class discussion, Mr. Martinez expects to see Nolan raise his hand and offer correct responses again. However, Nolan slumps in his seat, avoids eye contact, does not raise his hand to be called on, and when called on, offers no response. In regards to his class participation, praising Nolan served as


a.
negative reinforcement.
b.
positive reinforcement.
c.
presentation punishment.
d.
removal punishment.

Answers

Answer: c.  presentation punishment.

Explanation:

Presentation punishment involves adding an unpleasant or unwanted stimuli to a subject that will decrease the chances of them participating in the relevant activity again.

Praising Nolan must have been a presentation punishment to him that he did not want so in order to avoid being praised again, Nolan decides to avoid answering questions as he believes this will lead to the praise.

1. It is a decayed matter from plants and animals mixed with soil for plants to grow fast and become
productive.
a. Green Manure
b. Humus
c. Manure
d. Topsoil
2.
is cultivating the soil towards the base of the plant or
cultivation around the plant. When cultivation is done properly, the growth of weeds can be controlled.
a. Cultivating b. Hilling-up c. Off-barring
d. Planting
3. A way of supplying water to the plant from sources like deep wells, dams and rivers with the use of
motors or machine.
a. Advance watering b. Artificial watering
c. Manual watering d. Natural watering
4. This irrigation includes the line, rotating and micro sprinklers in which artificial rain is distributed through
special devices that wet the entire field
a. Drip irrigation b. Sub-irrigation c. Sprinkler irrigation d. Surface & furrow irrigation
5. A practice to help promote the growth of roots and improve aeration for fast absorption of nutrients by
the soil.
a. Cultivating the land b. Irrigating the land c. Preparing the land d. Watering the land
6. It is the most popular marketing tool to help organizations quickly draw the attention of prospective
customers.
a. Books
b. Brochures
c. Flyers
d. Magazines​

Answers

Answer:

D. Topsoil

C. Offbarring

B.Artificial watering

D.Surface & furrow irrigation

A cultivating the land

B. Brochures

Thorium-234 has a half-life of 24 days. How many grams of thorium-234 would remain from 100 g after 72 days? Show your problem-solving technique.

Answers

Answer:

[tex] \underline{ \boxed{12.5 g }}\: of \: (thorium-234 ) \\ \: would \: remain \: from \: \\ 100 g \: after \: 72 \: days[/tex]

Explanation:

[tex]if \: (Thorium-234) \: has \: a \: (half-life )\: of \: 24 \: days \\ then \: : it \: will \: disintegrate \: into \: \frac{1}{2} \: of \: 100g \\ but \: after \: 72 \: days \: i.e \: (24 \times 3)days \\ it \: will \: reduce \: to\:half \: its \: original \: ( \times 3) \\ hence \to \: \\ \frac{100}{ {2}^{3} } = \frac{100}{8} = \frac{25}{2} = \underline{ \boxed{12.5g}}[/tex]

Which of the following pairs of angles is not necessarily congruent

Answers

Answer:

E. [tex]\angle 3[/tex] and [tex]\angle 5[/tex].

Explanation:

According to the figure, we have the following conclusions:

1) [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are vertical opposite angles. ([tex]m \angle 1 = m \angle 2[/tex])

2) [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are internal alternate angles. ([tex]m \angle 2 = m\angle 3[/tex])

3) [tex]\angle 2[/tex] and [tex]\angle 4[/tex] are corresponding angles. ([tex]m\angle 2 = m\angle 4[/tex])

4) [tex]\angle 3[/tex] and [tex]\angle 4[/tex] are vertical opposite angles. ([tex]m \angle 3 = m \angle 4[/tex])

But, [tex]\angle 3[/tex] and [tex]\angle 5[/tex], since [tex]m \angle 3 + m\angle 6 + m\angle 5 = 180^{\circ}[/tex], where [tex]\angle 3[/tex] is an acute angle and [tex]\angle 6[/tex] is a right angle, and [tex]m \angle 4 + m \angle 5 = 90^{\circ}[/tex]. Then,

[tex]m\angle 5 = 90^{\circ} -m\angle 4[/tex].

[tex]m\angle 5 = 90^{\circ}-m\angle 3[/tex]

Hence, the right answer is E.

What makes a school formal organization

Answers

Answer:

A school has the following formal structure:

The school board acts as an agent of wider community. Frankly speaking, the school is a complex web of social interactions with various types of interactions taking place simultaneously, each affecting the whole, and having at least an indirect influence upon the child.

Answer:

School organizations, just as other organizations, have formally stated goals, criteria for membership, a hierarchy of offices, and a number of informal goals, such as friendship and sharing of interests.

I hope it's helpful!

The author regards the river as
A a friend.
B an obstacle.
C an inspiration.
D a threat.

Answers

More information is needed to solve this question
We need more information about this

Students have to pay to go to
O kindergarten
O high school
O middle school
W
O private school
Other:

Answers

Private $$$$$$$$$$$$$$$$$$$$$$$$$$
Private school has to be paid for

Which of the following scenarios would be considered an unconstitutional use of state power? Choose 1 answer: Choose 1 answer: (Choice A) A Imposing a sales tax on all clothing and cosmetics sold within a state (Choice B) B Establishing a minimum drinking age of 18 in their state (Choice C) C Requiring Amish students to attend school until age 16 despite their religious beliefs (Choice D) D Requiring a one-year waiting period before married couples can file for divorce

Answers

Answer:

D huhu

Explanation:

I think im not sure

Answer:

C: Requiring Amish students to attend school until age 16 despite their religious beliefs.

Explanation:

Doing this would be considered an unconstitutional use of power, as it does not follow the constitution

In U.S., children usually have to go to school when they are
O three years old
о
four years old
five years old
six years old
O
Other:

Answers

Explanation:

In the USA, children start school when they are five or six years old. Depending on the state, schooling is compulsory until the age of 16 or 18. Children younger than five can go to a nursery school or preschool.

It’s usually 5 years old

Smiling is to feeling as ________ is to ________.

Answers

Smiling it to feeling as Behavior is to Mental Process.

The writer wants to add an additional body paragraph to support the passage’s argument. Which of the following claims would make the best topic for such a paragraph

Answers

Answer:

E. Long-term missions would also create social and psychological issues, such as extreme isolation and loneliness, that may have a negative impact on space travelers.

Explanation:

Answer E

Correct. The writer supports the passage’s argument that long-term space travel is not likely to be viable or desirable in the near future by presenting reasoning and commentary in the body paragraphs pertaining to the negative effects space travel has on the physical well-being of humans—effects that are worsened the longer people spend in space. The best topic for an additional body paragraph among the choices provided is the one that addresses the negative consequences that long-term space travel would have on humans’ social and psychological well-being. This choice would provide additional support for the writer’s argument that there are too many serious concerns about long-term space travel for it to be viable in the near future.

Answer:

E. Long-term missions would also create social and psychological issues, such as extreme isolation and loneliness, that may have a negative impact on space travelers.

Explanation:

i just took the test

Which of the following statements best explains the trend shown in the data?

a. State governments tend to be more responsive to social movements than the federal government because they are able to test out new programs on a smaller scale.
b. The growth of social media has enabled movements to accelerate the acceptance of social change at the state level, because these activities are not as successful at the federal level.
c. A social movement needs to be approved by a percentage of the states before the federal government will consider acting on the change because of fear of angering the conservative electorate.
d. The federal government refuses to use the federal courts to respond to social-reform movements.

Answers

Hello there!

The correct answer is A:

State governments tend to be more responsive to social movements than the federal government because they are able to test out new programs on a smaller scale.

It is my pleasure helping students here!

~Garebear

Which of the following can be considered a military alliance? (2 points)
Kyoto Protocol
NAFTA
NATO
United Nations

a
I only

b
III only

c
I and II

d
I, II, and III

e
II, III, and IV

Answers

Answer:

B. III only (NATO)

Explanation:

In U.S., children usually have to go to school when they are
three years old
four years old
five years old
six years old
Other:

Answers

Answer:

Hmm... I think that's a trick question. I know in Pennsylvania, kindergarten is technically not required and kindergarten is when kids are 5 turning 6 so I'm guessing it's other. I'm not totally sure. Sorry, but I hope this helps!

which of the following defines chicago's position in relation to the infrastructure of the united states

Answers

Answer: situation

Explanation: It’s in RELATION to something

The option that defines Chicago's position in relation to the infrastructure of the United States is situation.

What is seen as infrastructure in the United States?

Infrastructure is known to be any of the basic amenities such as public and private physical structures that has been created e.g. roads, etc.

Conclusively, Note that The option that defines Chicago's position in relation to the infrastructure of the United States is situation as they believe that that infrastructure  is a situation that needs to be handled by the country.

See full options below

Which of the following defines Chicago's position in relation to the infrastructure of the United States?

answer choices

Site

situation

absolute location

vernacular region

transition

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shyla's resarch shows that 8 empty cans make 1/4 pound of aluminum. shayla wants to know how many cans it take to make 5 pounds of aluminum.

Answers

Explanation:
If 8 cans is 1/4 then 8 x 4 is 32 which is 4/4 or 1. 32 x 5 = 160

Answer:
160 cans

Answer:

If 8 cans is 1/4 then 8 x 4 is 32 which is 4/4 or 1. 32 x 5 = 160

Explanation:

160 cans

5. As discussed in the reading and in class, match the VB-MAPP component with its description. (5 pts)

A. Milestones Assessment D. Task Analysis & Skills Tracking
B. Barriers Assessment E. Placement & IEP Goals
C. Transition Assessment

_____ More comprehensive breakdown of skills to teach
_____ Identifies barriers that will impede progress
_____ Identifies specific skills to target
_____ Summarizes and provides specific directions
_____ Identifies overall skills and existing learning capabilities

Answers

Answer:

A) Milestones Assessment Identifies specific skills to target

B) Barriers Assessment identified barriers that will impede progress

C) Transition Assessment identified overall skills and existing learning capabilities

D) Task Analysis and Skills Tracking Summarizes and provides specific directions

Explanation:

The VB-MAPP means Verbal Behaviour Milestones and Placement Program.

It is a tool that is criterion-referenced that is created and intended for children with speech delays, children who are autistic, and other classes of individuals who have exhibited speech delay. It also contains a curriculum guide and a skill or progress tracking system.

Cheers


Jorge's production possibilities schedule demonstrates that
A. Green beans have a trade-off with corn, but corn does not have a trade-off with green beans
B. Green beans do not have a trade-off with corn, but corn has a trade-off with green beans
C. There is no trade-off between corn and green beans
D. Both corn and green beans require a trade-off

Answers

Answer: D. Both corn and green beans require a trade-off

Explanation:

Trade off simply means that for one to gain or have an increase with regards to a particular thing, thus will lead to the decrease or reduction in something else.

We should also note that the production possibility curve shows how two goods which are green beans and corn in this case can be efficiently used while making use of the resources that are made available for that particular economy.

In this case, we can see that as the pounds of green bean increase, the pound of corn reduces. This shows that both corn and green beans require a trade-off

who do we trust more the court or elected officials

Answers

Answer:

We trust the court more

Explanation:

Courts are the part of judiciary branch of governing constitution of any country. An individual can raise voice against injustice done to him/her by an elected official and further can reach out to the judiciaries body.

Judiciary system lies above the administrative system (comprising of  ministers or elected officials) and hence one has more trust on court than the elected officials.

The Everglades is a unique ecosystem of aquatic birds, plants and animals. For this area to thrive, it must be protected. Which of the following would have the least effect on the water flow through the Everglades?

A.) Planting trees that require an abundance of water for growth

B.) Constructing a road from the east to the west coast of South Florida

C.) Building irrigation canals for farmers to obtain water for their crops

D.) Overfishing of native species

Answers

Answer is c I took a guess sorry

Answer: it’s D

Explanation:

Because that has the least effect

Read the description of 1844 Manchester England and write a short advertisement for a real estate company that might encourage people to move or work there.

Answers

Answer:

Advertising is any paid form of communication from an identified sponsor or source that draws attention to ideas, goods, services or the sponsor itself. Most advertising is directed toward groups rather than individuals, and advertising is usually delivered through media such as television, radio, newspapers and, increasingly, the Internet. Ads are often measured in impressions (the number of times a consumer is exposed to an advertisement).

Advertising is a very old form of promotion with roots that go back even to ancient times. In recent decades, the practices of advertising have changed enormously as new technology and media have allowed consumers to bypass traditional advertising venues. From the invention of the remote control, which allows people to ignore advertising on TV without leaving the couch, to recording devices that let people watch TV programs but skip the ads, conventional advertising is on the wane. Across the board, television viewership has fragmented, and ratings have fallen.

Print media are also in decline, with fewer people subscribing to newspapers and other print media and more people favoring digital sources for news and entertainment. Newspaper advertising revenue has declined steadily since 2000.[1] Advertising revenue in television is also soft, and it is split across a growing number of broadcast and cable networks. Clearly companies need to move beyond traditional advertising channels to reach consumers. Digital media outlets have happily stepped in to fill this gap. Despite this changing landscape, for many companies advertising remains at the forefront of how they deliver the proper message to customers and prospective customers.

The Purpose of Advertising

Advertising has three primary objectives: to inform, to persuade, and to remind.

Informative Advertising creates awareness of brands, products, services, and ideas. It announces new products and programs and can educate people about the attributes and benefits of new or established products.

Persuasive Advertising tries to convince customers that a company’s services or products are the best, and it works to alter perceptions and enhance the image of a company or product. Its goal is to influence consumers to take action and switch brands, try a new product, or remain loyal to a current brand.

Reminder Advertising reminds people about the need for a product or service, or the features and benefits it will provide when they purchase promptly.

Explanation:

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When shooting a closeup shot, the subject should be approximately how far from the
background?

Answers

Answer: For example, a long shot refers to a shot that's taken at a distance from the subject with a long camera lens, while a low-angle shot refers to a shot taken from underneath the subject90-110mm – the standard macro focal length range; ideal for photographing flowers, insects and other small objects; . 150-200mm – a better option for mobile insects and other small animals because it provides more working distance . We also talked about the length of the camera lens above.

hope this helps have a nice day❤️

Explanation:

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