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)
A hacker .................... Into the government's website and replaced all the PM photos with his.
1 broken
2 broke
3 was breaking
4 was broking
The dog is fed by Juan. * 1 point ACTIVE VOICE PASSIVE VOICE
Answer:
The dog is fed by Juan
Passive voice
Explanation:
I guess passive voice is the ans
help please marking brainlist
Answer:
its the second option
Explanation:
a dog doesn't bury their bone it buries 'his' bond
i think :D
Answer:
B. I thought I saw a dog bury their bone under the tree.
Explanation:
The pronoun their is incorrect in this sentence. Their is used to describe ownership of something that belongs to a human. For example: The twins blew out the candle on their birthday cake. But, it does not describe ownership of something that belongs to an animal like a dog. The proper sentence would be (and the sentence could use his or her, but I will use his for this example): I thought I saw a dog bury his bone under the tree.
Hope this helps! :D
What advice does Martine give Sophie when Sophie asks her about liking someone?
Answer: um, that depends strongly on who he is, e.g friend, best friend, father, brother.etc
help me to find the tense please.
Answer:
1d, 2a,3b,4c,5b,6c
Explanation:
Please help will give brainliest
Answer: 1. circle the words u think are important
2. Then write abt what you think is an important thing to have on the camping trip.
3. Lastly write about what u would do during a camping trip.
Explanation:
I am comfused what part do u need help on?
sheela has to write a letter.( into yes/ no question)
Use these words to fill in the below:
abolish, bracket, breaks, Exempt, Exile, increase, property, return
1.The government needs more money, so it is planning to _____________________ taxes.
2. He earns a lot of money – he must be in the highest tax ______________________.
3. She lives there because she has to – she’s a tax _____________.
4. They are planning to _____________ the tax on large company cars, and replace it with a
tax on all company cars.
5. She is a student, so she is tax __________________.
6. The government is planning to introduce new tax ______________ for IT companies.
7. Don’t buy a house this year – the _________________ taxes are being abolished next March.
8. A tax ____________ is the same as a tax declaration – it’s a list of income and tax
deductible expenditure for
The government needs more money, so it is planning to increase taxes.
He earns a lot of money – he must be in the highest tax bracket.
She lives there because she has to – she’s a tax Exile.
What is tax?
The term tax refers to the government charge the extra money for goods and services. The tax is also called as financial charge. The amount of tax are collect to government account as spent on public welfare. The public pay tax is compulsory. There are two types of tax, such as direct tax and indirect tax.
According to the government requires more money are the rises the taxes.
Highest tax bracket, on the earn more.
She lives there because she has to – she’s a tax Exile.
They are planning to abolish the tax on large company cars, and replace it with a tax on all company cars.
She is a student, so she is tax exempt.
The government is planning to introduce new tax breaks for IT companies.
Don’t buy a house this year – the property taxes are being abolished next March.
A tax return is the same as a tax declaration – it’s a list of income and tax deductible expenditure for.
Learn more about on tax, here:
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Which lines from the poem indicate a change in focus of the speaker in let America be great again
Answer:
Let America be America again.
Let it be the dream it used to be.
Let it be the pioneer on the plain
Seeking a home where he himself is free.
Explanation:
Here you go let me know if I did something wrong :)
A storyboard is similar to?
A. a story book.
B. a comic book.
C. a movie
D. a wrriten scrip
Answer:
B.) Comic book.
Explanation:
Observe the attached image below, it is a storyboard. Notice how it looks like you are reading a comic book!
8) The author mentions caring for other kinds of pets
A)
to show how much care turtles need as well.
B)
to persuade against purchasing a pet turtle.
C) to explain that certain pets do not get along,
D) to illustrate how rewarding it is to own turtles,
Answer:
A
Explanation:
because it mentions caring for an animals in question A
In a single paragraph, describe what an abstract is.
1
SEE ANSWER
Your answer is - Overview. An abstract is a brief synopsis of your finished study. It is meant to summarize your work without going into too much detail. Abstracts should be self-contained and succinct, describing your work in as few words and as clearly as possible. A brief but precise statement of the problem or issue.
Hope that helps
Answer:
An abstract is a work of art using ones skill of creativity.
Explanation:
What is character development?
the ability to compare two different characters
a contrast between two characters’ backgrounds
whether a character is round or static
change that a character experiences throughout a story
Answer: The change a character experiences throughout a story.
Explanation: Character development is the process of building the character. What they did or had to go through that made them a part of what they are.
Read the excerpt from "Charles." With the third week of kindergarten Charles was an institution in our family; the baby was being a Charles when she cried all afternoon; Laurie did a Charles when he filled his wagon full of mud and pulled it through the kitchen; even my husband, when he caught his elbow in the telephone cord and pulled telephone, ashtray, and a bowl of flowers off the table, said, after the first minute, "Looks like Charles." What does the phrase "Charles was an institution in our family" imply about Charles? Charles has begun spending a great deal of time with Laurie's family. The personalities of Laurie's family members are just as difficult as Charles'. Charles's influence has caused the family to act in ways that are disruptive or destructive. Charles has become a very big part of the family's day-to-day life.
Answer:
Charles has become a very big part of the family's day-to-day life.
Explanation:
Answer:
Charles has become a very big part of the family's day-to-day life.
Explanation: i took the test
6. Which writing tip refers to developing the middle part of an essay?
O a. Always keep your thesis statement in mind,
O b. Summarize your main points.
O c Make a bold statement
Answer :
Summarize your main points.PLEASE PROOFREAD WILL MARK BRAINLIEST!
The benefits of starting school later
No one likes having to wake up early for school and as kids grow into their teenage years, they are forced to wake up even earlier as they move on from elementary school to middle school and high school. When students get older, it gets even harder to wake up and it leads to many obstacles that can be avoided by starting school at later times. By starting schools later, students have been shown to improve academically, be more productive, not skip school, and maintain better health. A later start time should be incorporated into schools everywhere, especially high schools, for the benefit of teenage students.
Grades are a very important aspect of education to many high school students, and grades are immensely dependent on adequate sleep. Later start times would allow for a greater quantity and quality of sleep. Poor sleep has a negative effect on a student’s academic performance. According to the Centers for Disease Control and Prevention (CDC), “Adolescents who do not get enough sleep are more likely to perform poorly in school”. Students who are not afforded the opportunity to get in the sufficient sleep they need will have a harder time focusing in school and doing well on exams. If schools were to push back the starting times in order to allow students to have a finer capacity of sleep, then the academic performance would improve, thus contributing to the common interest of all students.
Many teenagers fall victim to car accidents and poor attendance records. Later start times would mean an improvement in attendance and safety as fewer students would sleep in or fall under the risk of driving to school in drowsy conditions. Enabling students to sleep more would cause more students to come to school on time and make them less likely to drive to school in a fatigued state. The Science Daily revealed that “[...] later school start times were associated with a significant drop in vehicle accidents involving teen drivers”. This could be tied to the fact that teens are in a more rushed mood to get to school on time from waking up late or that they are driving while tired, which can lead to many dangers. By starting schools at later times, the risks of teen car accidents would be reduced and the overall attendance would improve, thereby allowing for the betterment of students in all places
Even with all the benefits of starting school at later times, there still remain those who challenge the idea. A common counterargument from the individuals in opposition to pushing back the schools’ starting times is that students should just sleep earlier. However, research has demonstrated that teenagers are biologically more likely to fall into a deeper sleep at later times. Science advocates say that “young people's body clocks may shift as they reach their teenage years - meaning they want to get up later not because they are lazy but because they are biologically programmed to do”. The biological clock of a teen does not correspond well with the schools’ starting times, and when a student is forced to wake up too early they are neglecting crucial parts of their sleep. In order to align better with teenagers’ internal clocks, schools should start at later times, which in return would result in the improvement of learning, concentration, and health.
Students commit a large portion of their day towards school and it would be a more enjoyable process if schools were to start at a more seemly time. For the general welfare of students in public education, the school start times should be moved to later times. The benefits include better grades, fewer absences, safer roads, and increased attentiveness. There is additional potential to starting schools later, such as the reduction of risk in athletics, less depressive symptoms, and a decrease in the likelihood of participating in violence. The further possibilities can only be explored as more schools start pushing back their start times and in the idealistic future, schools will hopefully start to implement a delay to start times as it is better for everyone.
Answer:
The benefits of starting school later
No one likes having to wake up early for school and as kids grow into their teenage years, as they are forced to wake up earlier as they move from elementary school to middle school and then high school. When students get older, it gets even harder to wake up and it leads to many obstacles that can be avoided by starting school at later times. By starting schools later, students have been shown to improve academically, be more productive—not skip school—and maintain better mental and physical health. A later start time should be incorporated into schools everywhere, especially high schools, for the benefit of the students.
Grades are a very important aspect of education to many high school students, and grades are immensely dependent on adequate sleep. Later start times would allow for a greater quantity and quality of sleep. Poor sleep has a negative effect on a student’s academic performance. According to the Centers for Disease Control and Prevention (CDC), “Adolescents who do not get enough sleep are more likely to perform poorly in school”. Students who are not afforded the opportunity to get the sufficient sleep (they need) will have a harder time focusing in school and doing well on exams. If schools push back the starting times in order to allow students to have a finer capacity of sleep, then the academic performance would improve, thus contributing to the common interest of all students, and teachers alike as they want their students to succeed.
Many teenagers fall victim to car accidents and poor attendance records. Later start times mean an improvement in attendance and safety as fewer students would sleep in or fall under the risk of driving to school in drowsy conditions. Enabling students to sleep more would cause more students to come to school on time and make them less likely to drive to school in a fatigued state. The Science Daily revealed that “later school start times were associated with a significant drop in vehicle accidents involving teen drivers”. This could be tied to the fact that teens are in a rushed mood to get to school on time from waking up late or that they are driving while tired, which can lead to many dangers. By starting schools at later times, the risks of teen car accidents would be reduced and the overall attendance would improve, thereby allowing for the betterment of students in all places
Even with all the benefits of starting school at later times, there still remain those who challenge the idea. A common counterargument from the individuals in opposition to pushing back the schools’ starting times is that students should just sleep earlier. However, research has demonstrated that teenagers are biologically more likely to fall into a deeper sleep at later times. Science advocates say that “young people's body clocks may shift as they reach their teenage years - meaning they want to get up later not because they are lazy but because they are biologically programmed to do”. The biological clock of a teen does not correspond well with schools’ starting times, and when a student is forced to wake up too early they are neglecting crucial parts of their sleep. In order to align better with teenagers’ internal clocks, schools should start at later times, which—in return—would result in the improvement of learning, concentration, and health.
Students commit a large portion of their day towards school and it would be a more enjoyable process if schools were to start at a more seemly time. For the general welfare of students in public education, the school start times should be moved to later times. The benefits include better grades, fewer absences, safer roads, and increased attentiveness. There is additional potential to starting schools later, such as the reduction of risk in athletics, less depressive symptoms, and a decrease in the likelihood of participating in violence. The further possibilities can only be explored as more schools start pushing back their start times and in the idealistic future, schools will hopefully start to implement a delay to start times as it is better for everyone.
Explanation:
I proofread it for you, and changed some things. I hope you find it useful!
According to the passage, which of the following is a lesson learned the Detroit automakers?
Answer:
They learned from tesla the fact of making sustainable cars.
Explanation:
Electric cars are objects of desire
what is the relationship between leaf and tree
Answer:
A leaf is a part of the tree while the tree is the organism it self
Which of the following literary devices may be used by an author to establish tone?
consonance
word choice
repetition
punctuation
heterophone
Answer:
Word Choice. An author may beautifully arrange words to create imagery which in turn creates tension or atmosphere of love. This dramatic effect relies heavily on the use of words which is also known as diction.
put cost in sentence in past simple
Answer:
Costed
Explanation:
It costed me a few seconds of my life to type this so please give brainliest
Answer:
costed
Explanation:
The simple past tense is used to talk about a completed action in a time before now. The simple past is the basic form of past tense in English. The time of the action can be in the recent past or the distant past and action duration is not important.
Please write 1 sentence about this image.
please help me plsssssssss!
Answer:
Takes,transfers,He arrives,stays,leaves,He attends,He,studies,tries,goes,He has
Have a good day
1. c 2. b 3. a 4. a 5. d
HELPPPPPPPPP PLZZ ANYONE?
Is this person vs society/
Elena´s feeling towards her house is that she feels embarrassed that she lives in a place like El building. In paragraph 1, it states "At almost any hours of the day, El building was like a monstrous jukebox, blasting out salsas from open windows as the residents, mostly new immigrants just up from the island, tried to drown out whatever they were currently enduring with loud music." Elena feelings towards Eugene's house is that she was in love with the house and that she is fascinated by the house. According to paragraph 6, it says " I could see their kitchen table, the sink, and the store." Then in paragraph 28, it says " the yard was healthy edged around the little walk that led to the door. It always amazed me how Paterson, the inner core of the city has no apparent logic to its architecture small, neat, single residents like this one could be found right next to huge dilapidated apartment building like El building."
7. Key Ideas and Details: What is the relationship between Nature and Science
in this poem?
It should be noted that the relationship is that science makes the assumption that the things and events in nature follow regular patterns that may be understood through thorough, methodical investigation.
What is the relationship between science and nature?Nature can refer to both universal life and the physical world's manifestations. A significant, if not the only, component of science is the study of nature. Despite the fact that humans are a part of nature, human activity is frequently thought of as a distinct category from other natural occurrences.
Teaching our kids about the nature of science is important because it encourages independent thinking and encourages them to draw their own findings and explanations that take into account the scientific aspects of social science concerns.
Science makes the assumption that the things and events in the cosmos follow regular patterns that may be understood through thorough, methodical investigation. According to scientists, people may find patterns in all of nature by applying their brains and using tools that broaden their senses.
The complete question wasn't found. Therefore, the relationship between science and nature was given.
Learn more about nature on:
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Wattpad suggestions?
Answer: dude read smut
Explanation: if you like harry potter those are best
Answer:
writing or reading?
Explanation:
writing:
find a topic then think of the plot
reading:
fan-fic
romance
comedy
adventure
one-shot
or what seem interest to you
Let's say you are writing a summary of the Article. Which is most important to put in the summary? A. There is new technology to make space tourism happen. B. SpaceX is a company that has a ship called Starship. C. There are rockets that carry supplies to a space station. D. SpaceX is a company that builds reusable spaceships. PLEASE HELP!
Answer:
i would say
Explanation:
i would say A because it starts to lean you into the story and the word would start to spread fast
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Midterm
2
Antonio is a web content manager who has experience publishing his own blog. What company might be inte
OA.
a hospital looking to digitalize their records
OB.
a retail store that wants its own app
C.
a large mortgage company that wants an online newsletter
D.
a laptop manufacturer that wants to test new hardware
Reset
Next
Answer:
I would say C I hope this helps if not I'm sorry
Shakespeare in pop culture: pop culture is what we refer to as the cultural activities or commercial products reflecting, suited to, or aimed at the tastes of the general masses of people. pop culture can be films, television, music, artwork, video games, etc. Shakespeare frequently appears in pop culture. your task is to find a minimum of [3] pop culture references to Shakespeare to discuss in class. use this sheet to record your findings, and please feel free to think outside the box (the discussion will be much more interesting if we come in with different examples).
Answer:
Festivity, the carnivalesque, and reinvention and appropriation of Shakespeare by popular culture in certain cultural contexts to assert international and national values.
Explanation:
The festive background of Elizabethan England obviously had a great impact on its dramatic productions. Very much aware of the popular demands and eager to cater for them, companies and their playwrights were keen to draw their productions and inspiration from legends, traditions, and myths linked to celebrations from the calendar festivals. Drama, was primarily the most popular medium of entertainment, in comparison to poetry and prose, and the location and design (next to wh*rehouses and bear and bull-baiting arenas, or other animal fighting pits, which could take place even inside the theatres) of the playhouses tell us much about the kind of relationship they bore with popular crowds. “It is also clear that the theatre was not necessarily first and foremost a temple of high culture, but might be primarily a place for having fun, rather than an instrument of privileged communication” (Laroque 180).
In 2012, thirty-seven companies from thirty-seven different countries intend to perform their own Shakespeare versions at the Globe. The tone is of celebration, as the direction states on the first page of the festival program: “The Globe to Globe festival is a carnival of stories” (2012:1). The related themes of festivity and the carnivalesque, so essential in Shakespeare’s time and extensively discussed by François Laroque, are rescued and privileged side by side with the issue of translation. Translation has gained such importance and value that the program opens with an article entitled “Flexible Shakespeare - Dennis Kennedy considers the gains to be made in performing the Bard without his language.” We must also remember that the program is not aimed at scholars, but at ordinary spectators, either with little or with considerable academic knowledge of Shakespeare, which shows how translation and cultural diversity have now become part of everybody’s life.
Because of Shakespeare’s flexible status, of the fluidity of shifting categories, and of the possibilities of reinvention, appropriation, and adaptation, my position towards the concepts of culture, the popular, and their connection with Shakespeare is one that does not regard these relationships on the basis of levels, superiority, evaluation, and categorization of cultural expressions as ‘good’ or ‘bad’. These are instances of language, of social constructions, in constant exchange, shift, and negotiation.
High or erudite culture will be used corresponding to a sum of discourses based on academic criteria, literacy, formal higher education, privileged financial means, and therefore as belonging to a minority, generally holder of economic, social, and political power. Popular culture will refer to other than formal sources of knowledge, including traditional practices, folklore, customs, and oral transmission of memory, to communal values and essentially shared practices, as well as to a site of identification and vindication of identities.
Resource I Used:
Back to the roots: Shakespeare and Popular Culture in the 20th and 21st centuries
Website: Open Edition Journals
I hope this helps you in any shape or form.
Match the following Acts with the explanation of the Act.
Fee charged for using paper
Punishment for disobeying the Quartering Act
Tax on molasses, coffee, fabric
If Great Britain passed a law, then the colonists had to obey.
Required colonists to house the British soldiers
Took civil rights away from the colonists
A. Intolerable Acts
B. Quartering Act
C. Declaratory Act
D. Townshend Acts
E. Sugar Act
F. Stamp Act
Answer:
A. Intolerable Acts; Punishment for disobeying the Quartering Act.
B. Quartering Act; Required colonists to house the British soldiers
C. Declaratory Act; If Great Britain passed a law, then the colonists had to obey.
D. Townshend Acts; Took civil rights away from the colonists.
E. Sugar Act; Tax on molasses, coffee, fabric.
F. Stamp Act; Fee charged for using paper.
Explanation:
Intolerable Acts: Punitive laws passed by the British Parliament in 1774 after the Boston Tea Party. The laws were meant to punish the Massachusetts colonists for their defiance in the Tea Party protest in reaction to changes in taxation by the British Government.
Quartering Act: Required the colonies to house British soldiers in barracks provided by the colonies
Declaratory Act: Declaration by the British Parliament that accompanied the repeal of the Stamp Act (that they were in control basically).
Townshend Acts: Imposed duties on British china, glass, lead, paint, paper and tea imported to the colonies.
Sugar Act: British legislation aimed at ending the smuggling trade in sugar and molasses.
Stamp Act: Act of the Parliament of Great Britain which imposed a direct tax on the British colonies in America and required that many printed materials in the colonies be produced on stamped paper produced in London, carrying an embossed revenue stamp.