Understanding the Definition of Symmetric Difference

Set theory uses a number of different operations to construct new sets from old ones. There are a variety of ways to select certain elements from given sets while excluding others. The result is typically a set that differs from the original ones. It is important to have well-defined ways to construct these new sets, and examples of these include the union, intersection, and difference of two sets. A set operation that is perhaps less well-known is called the symmetric difference. Symmetric Difference Definition To understand the definition of the symmetric difference, we must first understand the word or. Although small, the word or has two different uses in the English language. It can be exclusive or inclusive (and it was just used exclusively in this sentence). If we are told that we may choose from A or B, and the sense is exclusive, then we may only have one of the two options. If the sense is inclusive, then we may have A, we may have B, or we may have both A and B. Typically the context guides us when we run up against the word or and we don’t even need to think about which way it’s being used. If we are asked if we would like cream or sugar in our coffee, it’s clearly implied that we may have both of these. In mathematics, we want to eliminate ambiguity. So the word or in mathematics has an inclusive sense. The word or is thus employed in the inclusive sense in the definition of the union. The union of the sets A and B is the set of elements in either A or B (including those elements that are in both sets). But it becomes worthwhile to have a set operation that constructs the set containing elements in A or B, where or is used in the exclusive sense. This is what we call the symmetric difference. The symmetric difference of the sets A and B are those elements in A or B, but not in both A and B. While notation varies for the symmetric difference, we will write this as A ∆ B For an example of the symmetric difference, we will consider the sets A {1,2,3,4,5} and B {2,4,6}. The symmetric difference between these sets is {1,3,5,6}. In Terms of Other Set Operations Other set operations can be used to define the symmetric difference. From the above definition, it is clear that we may express the symmetric difference of A and B as the difference of the union of A and B and the intersection of A and B. In symbols we write: A ∆ B (A ∠ª B) – (A ∠© B). An equivalent expression, using some different set operations, helps to explain the name symmetric difference. Rather than use the above formulation, we may write the symmetric difference as follows: (A – B ) ∠ª (B – A). Here we see again that the symmetric difference is the set of elements in A but not B, or in B but not A. Thus we have excluded those elements in the intersection of A and B. It is possible to prove mathematically that these two formulas are equivalent and refer to the same set.​ The Name Symmetric Difference The name symmetric difference suggests a connection with the difference of two sets. This set difference is evident in both formulas above. In each of them, a difference of two sets was computed. What sets the symmetric difference apart from the difference is its symmetry. By construction, the roles of A and B can be changed. This is not true for the difference between two sets. To stress this point, with just a little work we will see the symmetry of the symmetric difference since we see A ∆ B (A – B ) ∠ª (B – A) (B – A) ∠ª (A – B ) B ∆ A.

Taking a Look at Life with Lex - 770 Words

Life With Lex is a newly set-up retail establishment that will offer fashionable clothing for sale to women aging from eighteen to fifty years old. Life With Lex is a sole proprietorship small business that will be located in uptown Kingston, New York. The uptown area of Kingston is becoming an extremely popular shopping area for locals because of its hip, vintage feel. While my inceptive goal is to open one boutique in uptown Kingston, my extension plans include inherently franchising my boutique Life With Lex, and/or the premises I am located in, a highly-acknowledged brand name. In the future, I would truly hope to occupy a substantial portion of the online retail market. The small business venture that I own and operate, a boutique named Life With Lex, is the perfect establishment for women to purchase products ranging from stylish clothing all the way to useful accessories. Flourishing businesses have a common characteristic in that they do something serviceable for their cu stomers. Therefore, if I precisely understand customer problems and needs, my business will have a better chance of triumph. My target market for my boutique Life With Lex is women aged from eighteen to fifty years old. Within this thirty-two age range, there are working class women and college students. Being in this particular age range, I personally know and fully understand that working class and college women like to buy fashionable, stylish clothing and other vaguely conservativeShow MoreRelatedDescriptive Essay - Original Writing2207 Words   |  9 Pagesextremely wacky right now, I need to chill with all the symbolism and figure out where I am. I look up from where I am sitting, well rather trapped, and start to scan the area I am in. 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Speaking In The Context Of New Zealand †Myassignmenthelp.Com

Question: How Do Tenants Demonstrate That They Have Ontological Security? Answer: Introducation Speaking in the context of New Zealand, Ontological security is influenced by several factors like society, relations, gender. It seems that people depend largely upon the real estate agents for the house purchasing decisions. Apart from this, the female folk of the families takes the major decisions keeping in mind several emotional factors which as per them will keep the family secure. There are also different factors that affect the tenants while purchasing houses and some of these factors have been led down by Levy Lawrence Murphy. One among them is emotional and contextual behavior. It is also a proven fact that people tend to be happier in their own houses than the owner-occupied houses (Herald on Sunday, 2012). However, the question that arises is how much happier the people actually are. It is largely evident from the Herald On Sunday article, how much pain and tension the tenants of the state housing blocks often suffer through. This happens when their houses are seized away by the Government. It has been heard from various inmates like Glenda Connon, Moepai Temata, who were totally devastated with this news that they will have to vacate their houses soon and will be shifted elsewhere. They have no idea about the new places that they will be shifted to; hence they are haunted by thoughts of an unsure future. (Miller, 2017) Using material from Murphy and Levy (2012) and Levy et al. (2008), critically examine the notion that housing markets are rational. House purchasing is one of the very crucial decisions that people take in their lives. It is also important because people have to invest their lifelong savings in this. Hence, the property estate agents say that house purchasing decision is one of the most rational decisions that people take in their lives. This decision is also self-regulating, in other words, it is something that depends wholly on the decisions of the purchasers (Levy, Murphy Lee 2008). As per the opinion of the real estate agents of New Zealand is concerned, they say that the adult female members usually make the final selection of the properties. It is also quite rational because they give much priority to the emotions and the family requirements. It is only after she has found a home that she considers to be right for all the family needs, she asks her husband to visit it. The husbands are usually busy working and do not get much time to visit the houses. However, in the contemporary families, the decision-mak ing process is dominated either by women or by both men and women. In the traditional families, one usually will see the opposite scene, as the male members dominate the entire decision-making process, keeping in mind the logical factors and ignoring the emotional factors. It has been said that the traditional families tend to make more rational house purchasing decisions (Levy, Murphy Lee 2008). It can also be said from this paper, that people are often driven by the opinions of their relatives or several other social constraints while buying a house. In other words, there are instances when buyers are influenced more by emotions, rather than the actual real facts and possibilities. However, the agents are of the opinion that these emotion-driven decisions are not necessarily irrational and can often turn out to be very meaningful. There has been a thorough session of interviews both with the families and the house agents regarding the rationality of the decision-making factors. B oth sets of interviews conclude that feelings and emotions do play a major role in the final decision-making process regarding the house purchasing. These decisions are often meaningful and rational. At the end, people take into consideration all the general factors. This makes the house purchasing decision very justified and rational. Critically discuss the difference between irrational exuberance and calculative affection in housing markets. Housing Market is very special and different than several other forms of markets. Irrational Exuberance is when the decisions in the housing market are affected more by the emotions of the investors. It often happens due to over excitement and often due to fear. The investors take decisions that may turn out to be very much unfavorable for them. It basically refers to the state when the price of the houses in the housing market is not functioning properly. It does not go in line with the national housing market expectations but is influenced by the emotions of the investors (Miller, 2017). Emotions and feelings play a major role here than the justified and working reasons. On the other hand, the calculative affections are something that works on the principle of taking into consideration those reasons that are more logical in nature. They are price, future expectations etc whereas the emotional factors that often affect the purchasers decisions are- close proximity to the laundry, hospital, sufficient place for accommodating all the family members. Reference list Fox O'Mahony, L. (2013). The meaning of home: from theory to practice.International Journal of Law in the Built Environment,5(2), 156-171. Herald on Sunday. (2012, March 4). The great betrayal of our poorer folk. New Zealand Herald. Retrieved from https://www.nzherald.co.nz/nz/news/article.cfm?c_id=1objectid=10789607. Levy, D., Murphy, L., Lee, C. K. (2008). Influences and emotions: exploring family decision-making processes when buying a house.Housing Studies,23(2), 271-289. Miller, C. (2017, April 15). Home truths: False hopes and downsized dreams. New Zealand Herald. Retrieved from https://www.nzherald.co.nz/residential-property/news/article.cfm?c_id=76objectid=11836224

The Trail of Tears, was it unjust and inhumane Wh Essay Example For Students

The Trail of Tears, was it unjust and inhumane? Wh Essay at happened to the Cherokee during that long and treacherous journey? They were brave and listened to the government, but they recieved unproductive land and lost their tribal land. The white settlers were already emigrating to the Union, or America. The East coast was burdened with new settlers and becoming vastly populated. President Andrew Jackson and the government had to find a way to move people to the West to make room. President Andrew Jackson passed the Indian Removal Policy in the year 1830. The Indian Removal Policy which called for the removal of Native Americans from the Tennessee, North Carolina, South Carolina, and Georgia area, also moved their capital Echota in Tennessee to the new capital call New Echota, Georgia and then eventually to the Indian Territory. The Indian Territory was declared in the Act of Congress in 1830 with the Indian Removal Policy. Elias Boudinot, Major Ridge, and John Ridge and there corps accepted the responsibility for the removal of one of the largest tribes in the Southeast that were the earliest to adapt to European ways. There was a war involving the Cherokee and the Chickasaw before the Indian Removal Policy was passed. The Cherokee were defeated by them which caused Chief Dragging Canoe to sign a treaty in 1777 to split up their tribe and have the portion of the tribe in Chattanooga, Tennessee called the Chickamauga. Chief Doublehead of the Chickamauga, a branch of the Cherokee, signed a treaty to give away their lands. We will write a custom essay on The Trail of Tears, was it unjust and inhumane? Wh specifically for you for only $16.38 $13.9/page Order now Tribal law says Death to any Cherokee who proposed to sell or exchange tribal land. Chief Doublehead was later executed by Major Ridge. Again there was another treaty signed in December 29, 1835 which is called The Treaty of New Echota. It was signed by a party of 500 Cherokee out of about 17,000. Between 1785 and 1902 twenty-five treaties were signed with white men to give up their tribal lands. The Cherokee would find themselves in a nightmare for the next year. In 1838 General Winfield Scott got tired of delaying this longer than the 2 years he waited already so he took charge in collecting the Cherokee. The Cherokee were taken from their homes and their belongings. The were placed in holding camps so none would escape. The Cherokee were to be moved in the fall of 1838. The journey did not occur in October, 1838 because of bad weather. They were now supposed to move 13,000 Cherokee in the spring of 1839 a distance of eight-hundred miles. The Cherokee were fed on meager rations and suffered malnutrition. They were badly clothed for the spring and many caught diseases and died. Many Cherokee tried to escape and some succeeded. The Cherokee knew these woodlands and knew where to go. The white men couldnt find them without the help of other Cherokee and bribes. Most of the Cherokee hid in the mountains and could not be found. During the eight-hundred mile trek many children and spouses were separated from their families when the Government would split up the Cherokee into groups of 1,000 for ease of removal. About one-third of the original Cherokee they collected died in the holding camps and between the trek from the Southeast section of the Union to Indian Territory. They would have to learn a new way of life and adjust. They lost their negro slaves, and their possessions. The Cherokee were farmers, and the land was infertile. The land was meant for cattle raising, which they didnt know ho to do. .ud49eada72b0e2d7edbec506c6fe6cc17 , .ud49eada72b0e2d7edbec506c6fe6cc17 .postImageUrl , .ud49eada72b0e2d7edbec506c6fe6cc17 .centered-text-area { min-height: 80px; position: relative; } .ud49eada72b0e2d7edbec506c6fe6cc17 , .ud49eada72b0e2d7edbec506c6fe6cc17:hover , .ud49eada72b0e2d7edbec506c6fe6cc17:visited , .ud49eada72b0e2d7edbec506c6fe6cc17:active { border:0!important; } .ud49eada72b0e2d7edbec506c6fe6cc17 .clearfix:after { content: ""; display: table; clear: both; } .ud49eada72b0e2d7edbec506c6fe6cc17 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ud49eada72b0e2d7edbec506c6fe6cc17:active , .ud49eada72b0e2d7edbec506c6fe6cc17:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ud49eada72b0e2d7edbec506c6fe6cc17 .centered-text-area { width: 100%; position: relative ; } .ud49eada72b0e2d7edbec506c6fe6cc17 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ud49eada72b0e2d7edbec506c6fe6cc17 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ud49eada72b0e2d7edbec506c6fe6cc17 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ud49eada72b0e2d7edbec506c6fe6cc17:hover .ctaButton { background-color: #34495E!important; } .ud49eada72b0e2d7edbec506c6fe6cc17 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ud49eada72b0e2d7edbec506c6fe6cc17 .ud49eada72b0e2d7edbec506c6fe6cc17-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ud49eada72b0e2d7edbec506c6fe6cc17:after { content: ""; display: block; clear: both; } READ: Atom Model Evolution Essay They built a capital city called Tahlequah, and their nation was declared in September 6, 1839. Their culture was bred here along their new way of life. John Ross who was elected by the Cherokee as the President of the Cherokee nation in 1827 continues his roll in the land, shared with another seventy tribes. They had opened up schools in the Indian Territory to continue their education for their children. The first Cherokee school opened in 1801 when the people were learning their language. Their written language which consists of 85 characters, was said to be created by a Sequoia (1760-1843) , a Cherokee .