1 Elementary Set Theory
Notation:
{} enclose a set.
{1, 2, 3} = {3, 2, 2, 1, 3} because a set is not defined by order or multiplicity.
{0, 2, 4, . . .} = {x|x is an even natural number} because two ways of writing
a set are equivalent.
∅ is the empty set.
x ∈ A denotes x is an element of A.
N = {0, 1, 2, . . .} are the natural numbers.
Z = {. . . , −2, −1, 0, 1, 2, . . .} are the integers.
Q = {
m
n
|m, n ∈ Z and n 6= 0} are the rational numbers.
R are the real numbers.
Axiom 1.1. Axiom of Extensionality Let A, B be sets. If (∀x)x ∈ A iff x ∈ B
then A = B.
Definition 1.1 (Subset). Let A, B be sets. Then A is a subset of B, written
A ⊆ B iff (∀x) if x ∈ A then x ∈ B.
Theorem 1.1. If A ⊆ B and B ⊆ A then A = B.
Proof. Let x be arbitrary.
Because A ⊆ B if x ∈ A then x ∈ B
Because B ⊆ A if x ∈ B then x ∈ A
Hence, x ∈ A iff x ∈ B, thus A = B.
Definition 1.2 (Union). Let A, B be sets. The Union A ∪ B of A and B is
defined by x ∈ A ∪ B if x ∈ A or x ∈ B.
Theorem 1.2. A ∪ (B ∪ C) = (A ∪ B) ∪ C
Proof. Let x be arbitrary.
x ∈ A ∪ (B ∪ C) iff x ∈ A or x ∈ B ∪ C
iff x ∈ A or (x ∈ B or x ∈ C)
iff x ∈ A or x ∈ B or x ∈ C
iff (x ∈ A or x ∈ B) or x ∈ C
iff x ∈ A ∪ B or x ∈ C
iff x ∈ (A ∪ B) ∪ C
Definition 1.3 (Intersection). Let A, B be sets. The intersection A ∩ B of A
and B is defined by a ∈ A ∩ B iff x ∈ A and x ∈ B
Theorem 1.3. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Proof. Let x be arbitrary. Then x ∈ A ∩ (B ∪ C) iff x ∈ A and x ∈ B ∩ C
iff x ∈ A and (x ∈ B or x ∈ C)
iff (x ∈ A and x ∈ B) or (x ∈ A and x ∈ C)
iff x ∈ A ∩ B or x ∈ A ∩ C
iff x ∈ (A ∩ B) ∪ (A ∩ C)
The prefix retro-makes the phrase "retroactive tax" mean "pay taxes."
A. good
B. forward
C. back
D. new
Answer:
C. back
Explanation:
Taxation can be defined as the involuntary or compulsory fees levied on individuals or business entities by the government to generate revenues used for funding public institutions and activities.
The different types of tax include the following;
1. Income tax: a tax on the money made by workers in the state. This type of tax is paid by employees with respect to the amount of money they receive as their wages or salary.
2. Property tax: a tax based on the value of a person's home or business. It is mainly taxed on physical assets or properties such as land, building, cars, business, etc.
3. Sales tax: a tax that is a percent of the price of goods sold in retail stores. It is being paid by the consumers (buyers) of finished goods and services and then, transfered to the appropriate authorities by the seller.
The prefix retro-makes the phrase "retroactive tax" mean "pay taxes back." because retro connotes something that has happened in the past.
This ultimately implies that, the tax applies to income or transactions that have taken place in the past.
All are sound devices except
A.Consonance
B. Assonance
C. Alliteration
D. Idioms
Answer:
D. Idioms
Explanation:
The answer is D since we can cross out alliteration and assonance since those are well known ones. Consonance is also a known one, so that leaves us D. Idioms. You can also see from the following pictures, A through C are all there except Idioms.
They didn't reach an agreement
their differences.
on account of
due. because
owing
Answer:
They didn't reach an agreement on account of their differences.
Explanation:
In the given sentence, the necessary word(s) to be put in the blank will be suggestive of the 'cause' of the first part of the sentence. While the first part contains the effect' of the 'cause', completing the whole sentence depends on the part or parts of the phrase needed.
The given options "on account of", "due", "because" or "owing" are all valid to be used in the given sentence. But considering the form and structure of the sentence, the blank will be filled by "on account of".
To use the other options, we would need to add more to the already given words. We cannot simply write "they didn't reach an agreement due/owing/because their differences." For "due" and "owing", it needs "to" to make the sentence whole. Likewise, "because" requires "of" to be usable. If we add these words to the already given words, then the sentence can become
they didn't reach an agreement due to/ because of/ owing to their differences. But these options are wrong as the words are incomplete.
Thus, the correct answer is "on account of".
They didn't reach an agreement on account of their differences.
The writer wants to change this passage so that it will be appropriate for doctors and other scientists rather than a general audience. In order to make the passage appropriate for the intended audience, which sentence is most necessary for the writer to delete?
A.Sentence 2
B.Sentence 5
C.Sentence 9
D.Sentence 11
E.Sentence 18
Which of these writing prompts is asking for a persuasive essay?
Answer:
Where are the prompts?? Attach photo
Why is a dwarf planet not classified as a planet?
It orbits larger planets.
It does not clear the neighborhood around its orbital.
It does not have enough mass to become spherical.
It does not orbit the Sun.
(see image above)
Note:Cite the website where you got the evidence.
NO LINKS OR YOU GET REPORTED!
Answer: just look up modern technology helps students learn and use the first link.
Explanation:
Identify Two possible reasons for unemployment
Answer:
can't work and can't get a job
Which sentence is the best example of alliteration?
O A. Tendrils of smoke clutched the bridge like fingers.
B. Doug doesn't do department duties diligently.
O C. Before you start to bake, / decide what to make.
D. The judge struck her gavel and said, "Overruled!"
Read the excerpt from "Lessons of Dr. Martin Luther King, Jr."
Economic pressure is the only language the growers speak, and they are beginning to listen.
Please, boycott table grapes.
Will give brainliest
Which persuasive element does Chavez use in this passage?
using words to connect with the audience
using facts to support an argument
stating a clear purpose or goal
creating a strong introduction
Answer:
The answer is C. stating a clear purpose or goal
Explanation:
I did the test on edge 2021
Answer:
C: Stating a clear purpose or goal.
Explanation:
Same as the guy above me.
I’m going To need your help on This no links on My question or I will report you
Answer:
1.D
2.C
3.C
4.B
Explanation:
1. Implode means to get smaller
2. Supernova is a stellar explosion
3. massive is large
4. light year is a time period
I need someone to find the one subject and verb in each sentence, appreciate it (I’ll reward points + brainalist)
Answer:
1. S - Allen V - watched
2. S - Marcus V - read
3. S - Mr and Mrs Valdez V - traveled
4. S - bag V - lend
5. S - The Bishops V - sing
6. S - Africa V - rain
Explanation:
Please brainliest!
In what ways are romeos and Juliet’s reactions to romeo’s banishment similar and different ?
Answer:
Romeo and Juliet are both upset. Both confide in their protector (friar and nurse), and go to the friar for help. Naturally, Romeo and Juliet are both upset when they realize that Romeo has been banished. They are young and in love, and cannot imagine how they will live apart.
Explanation:
Where is the best place to include background information about your topic, such as its history?
A. near the end, right before the conclusion
B. near the beginning, after the introduction
C. in the middle of your reasons and evidence
Answer:
B/ Near the beginning, after the introduction
Explanation:
I took the test and got it right
The best place to include background information about your topic, such as its history is near the beginning, after the introduction. Thus, option "B" is correct.
Where is the best place to include background information about your topic?Glossaries and encyclopedias wonderful are a place to start your study as they are obliging for finding definitions, outlines , background report and fundamental facts.
They may be widespread or subject specific, in print or online and may provide bibliographical references.
Thus, option "B" is correct.
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What is the order of most formal debates?
rebuttals, opposing team statement, affirmative team statement
affirmative team statement, opposing team statement, rebuttals
affirmative team statement, brief recess, opposing team statement
opposing team statement, brief recess, affirmative team statement
The order of most formal debates is affirmative team statement, opposing team statement, and rebuttals. The correct option is B.
What do you mean by a debate?A debate is a formal discussion or argument between two or more people who present their viewpoints or arguments on a particular topic or issue. The participants of a debate are typically divided into two teams or sides, with one team arguing in favor of a proposition or statement (the affirmative team) and the other team arguing against it (the opposing team).
Debates can be structured in different ways, but typically involve a series of speeches or statements from each team, followed by rebuttals, cross-examinations, and closing statements.
The goal of a debate is to persuade the audience and judges that one side's arguments are more compelling and supported by evidence than the other side's. Debates can be held on a wide range of topics, from political and social issues to academic and philosophical debates.
There may also be additional rounds of rebuttals and cross-examinations depending on the format of the debate. A brief recess may be taken between rounds, but it is not typically part of the formal order of the debate.
Therefore, The correct order of most formal debates is Affirmative team statement, Opposing team statement, and Rebuttals.
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Select the correct answer. Which example is the correct citation for a book? A. Rothbart, Davy. "How I Caught Up with Dad." Men's Health Oct. 2008: 108-13. Print. B. Sutter, J. D. (2010, March 31). Why Internet Connections Are Fastest in South Korea. CNN Tech. Retrieved from http://cnn.com C. Austen, Jane. Pride and Prejudice. New York: Modern Library, 1995. Print. D. Bowman, Lee. "Bills Target Lake Erie Mussels." The Pittsburgh Press, March 7, 1990.
Answer:
The answer for this question would be C. Austen, Jane. Pride and Prejudice. New York: Modern Library, 1995. Print.
Explanation:
Question 6
READ ITI
What happens because Kylo tries to get attention instead of being a
team player?
Nico scores the winning goal,
He is not voted Most Valuable Player
Jamol becomes the team's highest scorer
His team loses to the Cougars
Explanation:
he was not voted most valuable player
What is Lewis Carroll's attitude toward Humpty
Dumpty? How can you tell?
O Humpty Dumpty is very smart. He knows a lot
about words.
Humpty Dumpty is a bit of a know-it-all. He thinks
words mean whatever he wants them to mean.
Humpty Dumpty is friendly. He smiles at Alice.
Humpty Dumpty is helpful. He teaches Alice the
meaning of words.
It’s B !
Lewis carroll's attitude towards Humpty Dumpty is that D. Humpty Dumpty is helpful. He teaches Alice the meaning of words.
In Lewis Carroll's rendition, Humpty Dumpty is a wordsmith who is fascinated with expanding his vocabulary and not just reciting but also explaining poetry to Alice. He is completely fixated on the idea of being able to force meaning. He uses words to signify anything he wants and justifies it by stating he can always pay more on the weekends. His behavior serves as a reminder that, although being manipulable, meaning cannot be coerced.
Who is Lewis Caroll?
Lewis Carroll, the pen name of English author, poet, and mathematician Charles Lutwidge Dodgson, was born in London. His best-known books include Through the Looking-Glass, the sequel to Alice in Wonderland, and Alice in Wonderland. He was praised for his aptitude for word play, logic, and fantasy.
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Try These out and I’ll give you brainliest no links posted on My question or I will report you
Answer:
1 b
2 c
3 c
4 b
Hope this helps you!
Answer:
ok
1 a
2 b
3 c
4 c
Explanation:
Who is Mrs. W? What is her lifestyle like, and what does she expect of the maids? how does she treat Ehrenreich
Answer:
is this a question related to a book
Explanation:
How does increasing the minimum wage help teenager and people struggling with jobs?
Answer:
Increasing minimum wage helps people struggling by making the mandatory pay higher, allowing people to have more money.
Above is the answer whoever put out this question wants. But it would be good for you to know that it actually doesn't help people by increasing minimum wage. It increases the amount of money that companies must pay their workers, which sounds good until you realize that when put into practice, all this does is force companies to either go out of business or fire it's workers. If the minimum wage increases, it will lead to more people struggling. It will lead to more companies failing and more people going into poverty. But this is not the answer that is wanted.
indirect characterization
Indirect characterization is the process of describing a character through that character's thoughts, actions, speech, and dialogue. An author will use this type of characterization to guide the reader in making their own conclusions about a character.
I need help with this right now please somebody help me
Answer:
Number 1
Explanation:
It mostly talks about looking at the countryside and imagining doing things such as flying in the wind. Sorry if im wrong haha
My heart, your heart
Sit tight like bookends
Pages between us
Written with no end
So many words we're not saying
Don't wanna wait 'til it's gone
You make me strong
I'm sorry if I say, "I need you"
But I don't care, I'm not scared of love
'Cause when I'm not with you, I'm weaker
Is that so wrong? Is it so wrong
That you make me strong?
Think of how much
Love that's been wasted
People always
Trying to escape it
Move on to stop their heart breaking
But there's nothing I'm running from
You make me strong
I'm sorry if I say, "I need you"
But I don't care, I'm not scared of love
'Cause when I'm not with you, I'm weaker
Is that so wrong? Is it so wrong?
Answer:
wow, i love your song! what do you think of mine (its a poem) ?
Explanation:
From the dark side of the moon
I shall send you a letter
And hope it will be there soon
From the footsteps left here
They will only appear
Only once a year
When my love comes
And she will become
A flower in May
Shining all day
Filled with happiness
And gets her own way
But when she is gone and the whole world seems wrong
So dull and gray
Will be the last breath I breathe
And oh the joyness it brings
To finally see my girl
Who couldn’t gave a care in the world
With her little strand of hair
Always making a little curl
And she didn’t have to give a twirl
Nor a swirl
Nor whirl
She’s my pearl
That little girl
My pearl girl
How does Thoreau support his claim in this excerpt?
A.
He uses reasoning, showing the logical consequences of supporting a cause that is wrong.
B.
He tells an anecdote about a townsman who refused to “march to Mexico” and what happened to him.
C.
He shares statistics about casualties in the Mexican-American War.
D.
He uses measurable evidence about the number of people who have refused to join the US Army.
Answer:
this isn't an answer but I'm wondering as well, I'm terrible at English and I think it sucks.
Explanation:
i could be c
Thoreau supports his claim in this excerpt: He shares statistics about casualties in the Mexican-American War. Thus, option C is the correct option.
What was Thoreau's main focus?Thoreau offers distinctive contributions to ontology, the philosophy of science, and radical political thinking in addition to his emphasis on ethics in an existential sense. Although though his writings on natural science were not even published until the late 20th century, despite the justifiable fame of his political articles, they assist to paint a more full picture of him as a thinker.
A series of manuscript volumes containing information on Native American religion and culture was one of the manuscripts he left incomplete. Thoreau's writings represent a perennially valuable challenge to our understanding of the processes and goals of philosophy itself and foreshadow certain subsequent advances in pragmatism, phenomenology, and environmental philosophy.
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Try These questions out and I’ll give you brainliest no links posted on My question or I will report you
Read this excerpt from We’ve Got a Job.
At that moment, nine-year-old Audrey made a decision. She would no longer just attend meetings. Somehow, she would act on her own.
Which of Audrey’s character traits is best highlighted in this excerpt?
her curiosity
her independence
her stubbornness
her cleverness
Answer: Independance
Explanation: I’ll give you a hint, acting on your own means your acting independantly Therefore when Audrey is acting on her own she is acting independently. (Sorry for bad spelling)
Answer:
b
Explanation:
in a group discussion, which of these is the best example of a clarifying question
Answer:
D. When you say H. G. Wells lacked genius, how are you defining "genius"?
If that's one of your choices, because out of the four options, option letter D, presents the example of a question that is asking to clarify upon the meaning of a word, in this case, the word "genius". Clarifying information is important to guarantee the understanding of the idea.
why immigration reform is needed in America.
Answer/Explaination:
In fact, immigrants contribute to the U.S. economy in many ways. They work at high rates and make up more than a third of the workforce in some industries. Their geographic mobility helps local economies respond to worker shortages, smoothing out bumps that could otherwise weaken the economy.
What is the function of an interjection?
A. To tell a location or time
B. To join two ideas in a sentence
C. To describe a verb or a noun
D. To show emotion or feeling
The function of an interjection is to show emotion or feeling. They don't follow the remainder of the statement correctly. D is the right option.
The ads within the code you gave are utilized to communicate the taking after feelings:
Wow! - Shocking
Goodness no! - Stun
Goodness, expensive! - Astonish
Here are some more pointers for efficiently using interjections:
Use them in moderation. It's crucial to utilize interjections cautiously since they might be misused. They will lose their impact if you use them excessively.
Use them to convey powerful feelings. Strong emotions are best expressed through interjections. You don't need to use an interjection if you're only a little bit joyful. However, if you're thrilled, adding an exclamation like "Hurray!" may dramatically improve your work.
Hence, the correct option is D. To show emotion or feeling
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