What Is the Power Set

What Is the Power Set One question in set theory is whether a set is a subset of another set. A subset of A is a set which is formed by using some of the elements from the set A. In order for B to be a subset of A, every element of B must also be an element of A. Every set has several subsets. Sometimes it is desirable to know all of the subsets that are possible. A construction known as the power set helps in this endeavor. The power set of the set A is a set with elements that are also sets. This power set formed by including all of the subsets of a given set A. Example 1 We will consider two examples of power sets. For the first, if we begin with the set A {1, 2, 3}, then what is the power set? We continue by listing all of the subsets of A. The empty set is a subset of A. Indeed the empty set is a subset of every set. This is the only subset with no elements of A.The sets {1}, {2}, {3} are the only subsets of A with one element.The sets {1, 2}, {1, 3}, {2, 3} are the only subsets of A with two elements.Every set is a subset of itself. Thus A {1, 2, 3} is a subset of A. This is the only subset with three elements. A A A Example 2 For the second example, we will consider the power set of B {1, 2, 3, 4}. Much of what we said above is similar, if not identical now: The empty set and B are both subsets.Since there are four elements of B, there are four subsets with one element: {1}, {2}, {3}, {4}.Since every subset of three elements can be formed by eliminating one element from B and there are four elements, there are four such subsets: {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}.It remains to determine the subsets with two elements. We are forming a subset of two elements chosen from a set of 4. This is a combination and there are C (4, 2 ) 6 of these combinations. The subsets are: {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}. B B Notation There are two ways that the power set of a set A is denoted. One way to denote this is use the symbol P( A), where sometimes this letter P is written with a stylized script. Another notation for the power set of A is 2A. This notation is used to connect the power set to the number of elements in the power set. Size of the Power Set We will examine this notation further. If A is a finite set with n elements, then its power set P( A ) will have 2n elements. If we are working with an infinite set, then it is not helpful to think of 2n elements. However, a theorem of Cantor tells us that the cardinality of a set and its power set cannot be the same. It was an open question in mathematics whether the cardinality of the power set of a countably infinite set matches the cardinality of the reals. The resolution of this question is quite technical, but says that we may choose to make this identification of cardinalities or not. Both lead to a consistent mathematical theory. Power Sets in Probability The subject of probability is based upon set theory. Instead of referring to universal sets and subsets, we instead talk about sample spaces and events. Sometimes when working with a sample space, we wish to determine the events of that sample space. The power set of the sample space that we have will give us all possible events.

Collaborating Community Nursing and Faith Based Nursing Essay

Collaborating Community Nursing and Faith Based Nursing - Essay Example In the same way community based entities offer sensitive patient care and high quality health care to cater for the diverse health care needs in the population. The idea of faith nursing is widely referred to as parish nursing was started in 1985 and has developed immensely to date into one of the most popular forms of the nursing practice in the community setting (DeHaven, 2004). The revolutionary concept works towards incorporating healing and faith and concentrates on promotion of health within the confines of the values, beliefs and practices of the church. More importantly the concept links parishioners to the church through the provision of respect and compassion to the basics of health care. Cooperation between faith-based communities and parish nurses is beneficial to all members of society especially those that are marginalized as well as those that have not been covered by a health insurance cover (Burns and Grove, 2010). To start with this cooperation facilitates access to health care mainly to the individuals that have been isolated in society. This includes the elderly, the homeless and individuals from minority groups in the population (DeHaven, 2004). For instance, a parish nurse visited an elderly woman who was locked up and was ailing from pneumonia and found that no one had visited her or even tried to call her in a period of two months. This is a highly common occurrence especially when dealing with homebound individuals that cannot access health care. This cooperation facilitates the development of a medical schedule through the warm presence of the parish nurses. They go ahead to explain the purpose of the schedule and the anticipated results (Burns and Grove, 2010). At the end of every session recite a prayer. This is important in the overall healing process as well as patient participation (DeHaven, 2004). The current health care

Dangerous Liaison Vs Cruel Intentions Coursework

Dangerous Liaison Vs Cruel Intentions - Coursework Example Cruel Intentions is a modern day adaptation of the novel with love, evil, gullibility and manipulation combined with moral cynicism and lust for domination by the primary protagonists. The main characters in the novel were French aristocrats and adults, while the movie depicts the protagonists as young adults who combine manipulation and revenge to achieve their ulterior goals. The lack of social and moral authority which is denounced by Laclos in the novel is transformed into the lack of parental influence on Catherine and Sebastian in the movie. The two siblings are free to pursue their dangerous game of playing with others’ feelings and reputations. The movie also has many erotic messages which create a mental image of what the protagonists is up-to. The novel on the other hand provides the action through a veil of language. Laclos establishes the hypocrisy of the main characters by a series of letters in which they show their various facets to different recipients. The mov ie highlights the hypocrisy of the lead characters in the opening credits as they get ready to mingle with society. Both Merteuil and Catherine are respected members of their societies without anyone their true nature. In Dangerous Liaisons, Valmont dies in a sword fight with Danceny. Before dying he gives him letters which would ruin the reputation of Merteuil. Her reputation is shattered and she eventually dies of misery. Cruel Intentions provides a more heroic and tragic ending of Sebastian who is killed in a car accident. He pushes Annette out of the care before being killed. Annette and Cecile ensure that Catherine is humiliated in front of the student body. Her drug addiction becomes public which tarnishes her reputation. The subject of drug abuse amongst young adults is a major theme of the movie. The movie also portrays the independence of modern women. Cecile and Annette fight back against the manipulation and deceit of

Components of Reading Essay Example for Free

Components of Reading Essay

Attila The Hun Essay -- essays research papers

Attila the Hun is known as one of the most ferocious leaders of ancient times. He was given the nickname â€Å"Scourge God† because of his ferocity. During the twentieth century, â€Å"Hun† was one of the worst name you could call a person, due to Attila. The Huns were a barbaric and savage group of people, and Attila, their leader, was no exception. He was the stereotypical sacker of cities and killer of babies. The Huns lasted long after their disappearance in mythology and folklore, as the bad guy. Generally, they were not fun people to be around. Priscus saw Attila the Hun at a banquet in 448. Priscus described him as being a short, squat man with a large head and deep-set eyes. He also had a flat nose and a thin beard. Historians say that his general personality was irritable, blustering, and truculent. He was said to be a persistent negotiator, and not at al pitiless. While Priscus was at the banquet in 448, he observed a few other details about Attila. All of Attila’s chief lieutenants were served dainties on silver platters, but he was served only meat on wooden plates. No other real qualities of Attila as a general really survived through time, but he is thought to have been an outstanding commander from his accomplishments as a barbarian. Huns themselves were mysterious and feared people. They first appeared in the Fourth Century around the Roman Empire. They rode their warhorses around and cause the Germanic barbarians and Romans alike to fear them. Yet, it was said that they were very uncivilized. It was said that they made no use of fire, and just ate the roots of plants they found in fields. They were also said to have eaten the almost raw meat of animals. The only reason the meat was â€Å"almost raw† was because they were said to have â€Å"cooked† it by placing it between their thighs and the backs of their horses to give it warmth. The Huns sometimes engaged in regular battle. They would attack in an order of columns, and scream very disorderly and savage cries. Most of the time, though, the Huns just fought in a very random way. They would scream and run about and then all come together in a large group. They would then, as a group, approach the camp or town of the people they were attacking, and destroy it. Most of the time, the people the Huns attacked never even saw them coming. There were many ways in which the Huns chose to fight. They often s... ...y. They sacked many cities, including Aquilieia, Patavium, Verona, Brixia, Bergomum, and Mediolamun. There wasn’t much Aetius could do about this. Luckily, famine and pestilence caused the Huns to leave before crossing the Apennines. In 453, Attila planned to attack the Eastern Empire because the Emperor wasn’t paying the money set in previous treaties (author’s note: Don’t these emperors ever learn anything?). Nothing ever actually came of these plans because, quite suspiciously, Attila died in his bed the night after his marriage. When Attila was buried, the Huns went through a lot of trouble. They had to kill anyone who was involved with the burial, so that no one would know of the exact place that Attila was buried. Attila was succeeded by his sons, between which the empire was divided. Attila didn’t have a huge impact on history, because the Romans very well could have done without him. He mainly caused trouble for the Romans, and killed a lot of innocent people just to get his way. Attila the Hun was one of the most important kings of the Huns, though, and he definitely has his place in history, as a barbaric, baby-killing, rude leader of a very ruthless group of warriors. Attila The Hun Essay -- essays research papers Attila the Hun is known as one of the most ferocious leaders of ancient times. He was given the nickname â€Å"Scourge God† because of his ferocity. During the twentieth century, â€Å"Hun† was one of the worst name you could call a person, due to Attila. The Huns were a barbaric and savage group of people, and Attila, their leader, was no exception. He was the stereotypical sacker of cities and killer of babies. The Huns lasted long after their disappearance in mythology and folklore, as the bad guy. Generally, they were not fun people to be around. Priscus saw Attila the Hun at a banquet in 448. Priscus described him as being a short, squat man with a large head and deep-set eyes. He also had a flat nose and a thin beard. Historians say that his general personality was irritable, blustering, and truculent. He was said to be a persistent negotiator, and not at al pitiless. While Priscus was at the banquet in 448, he observed a few other details about Attila. All of Attila’s chief lieutenants were served dainties on silver platters, but he was served only meat on wooden plates. No other real qualities of Attila as a general really survived through time, but he is thought to have been an outstanding commander from his accomplishments as a barbarian. Huns themselves were mysterious and feared people. They first appeared in the Fourth Century around the Roman Empire. They rode their warhorses around and cause the Germanic barbarians and Romans alike to fear them. Yet, it was said that they were very uncivilized. It was said that they made no use of fire, and just ate the roots of plants they found in fields. They were also said to have eaten the almost raw meat of animals. The only reason the meat was â€Å"almost raw† was because they were said to have â€Å"cooked† it by placing it between their thighs and the backs of their horses to give it warmth. The Huns sometimes engaged in regular battle. They would attack in an order of columns, and scream very disorderly and savage cries. Most of the time, though, the Huns just fought in a very random way. They would scream and run about and then all come together in a large group. They would then, as a group, approach the camp or town of the people they were attacking, and destroy it. Most of the time, the people the Huns attacked never even saw them coming. There were many ways in which the Huns chose to fight. They often s... ...y. They sacked many cities, including Aquilieia, Patavium, Verona, Brixia, Bergomum, and Mediolamun. There wasn’t much Aetius could do about this. Luckily, famine and pestilence caused the Huns to leave before crossing the Apennines. In 453, Attila planned to attack the Eastern Empire because the Emperor wasn’t paying the money set in previous treaties (author’s note: Don’t these emperors ever learn anything?). Nothing ever actually came of these plans because, quite suspiciously, Attila died in his bed the night after his marriage. When Attila was buried, the Huns went through a lot of trouble. They had to kill anyone who was involved with the burial, so that no one would know of the exact place that Attila was buried. Attila was succeeded by his sons, between which the empire was divided. Attila didn’t have a huge impact on history, because the Romans very well could have done without him. He mainly caused trouble for the Romans, and killed a lot of innocent people just to get his way. Attila the Hun was one of the most important kings of the Huns, though, and he definitely has his place in history, as a barbaric, baby-killing, rude leader of a very ruthless group of warriors.

Critically Evaluate the Case for Social Partnership Between Unions and Employers

Critically evaluate the case for social partnership between unions and employers The concept of social partnership originates from the Rhenish model of industrial relations. It has passed in to the British lexicon through the European Union. At a European level the social partners are trade unions and employers federations. However in the UK the employers peak federation the CBI has indicated that it is unwilling to fulfil such a role at a national level. Instead the Anglo-Saxon model of social partnership operates a company and workplace level. This essay will investigate the arguments for and against social partnership on the Anglo-Saxon model from the perspective of the employer and trade union. It will recognise that the criteria for judging the efficacy of social partnership differ between employers and unions. The case for social partnership from the employer perspective is ambiguous and will be contingent on management attitudes and business strategy. It will argue that while social partnership undoubtedly presents problems for trade unions it is by far the lesser of two evils when compared with individualised employee involvement and human resource management policies. Trade unions should promote partnership as an alternative ideology to capital driven unitarism. If implemented in the context of collective bargaining mutual gains principals offer a model for company level social partnership. Proponents of the mutual gains enterprise are quite clear that it is not a universally applicable prescription. To be made to work it requires high levels of investment in human resources, employees cannot be treated as just another cost, to be trimmed where possible. However companies willing to pursue ‘mutual gains’ policies benefit from increased productivity and creativity, and consequently higher profitability. Companies that are trying to compete purely on the basis of lowest cost would not be able to implement the principles. Kochan and Osterman marshal considerable case study evidence to support their theory. However at the moment the empirical research to validate it does not exist . Freidman (1977) has proposed that employer strategies towards the workforce are contingent on the economic cycle. When factors are favourable employers are more likely to emphasise policies with elements of employee involvement and greater trust that are likely to win loyalty and support of the workforce. While in times of recession, declining profitability and an unfavourable labour market positionemployers are more likely to fall back on authoritarian policies, cutting back wages and increasing supervision. This may provide a framework for understanding the conditions in which employers are prepared to enter into social partnership agreements. Kochan and Osterman offer the further hypothesis that mutual gains theory will work better if the enterprise recognises independent trade unions. They argue that union based voice mechanisms are more effective than the alternatives because they recognise that the interests of the workforce and the company will not always be in unison. Where conflicts do arise union voice mechanisms allow them to be negotiated and resolved without compromising the climate of co-operation and trust. This is not a view shared by everyone. Nestle provide an example of a company introducing HRM practices to achieve mutual gains objectives in parallel with traditional collective bargaining. In the long run Nestle management expect traditional industrial relations to wither away, replaced by individual relationships between the company and its employees. (Taylor, 1994:131). Given that there are conditions in which employers are more likely to pursue employee involvement policies I would offer the hypothesis that the union attitude is an important factor influencing the way in which an employer introduces HRM and employee involvement strategies. If the union is not prepared to work in partnership the employer may proceed with policies that would have the effect of de-collectivising the workforce and marginalising the union. If the union side are prepared to engage in partnership at a strategic level then the form of partnership may be considerably more favourable to unions and there members. There is currently no data available to test this hypothesis rigorously, however case studies may shed some light on the area.

Funny Marriage Quotes

Marriages may be made in heaven, but they sure have to be managed right here on earth. Thats easier said than done. Take a dig at the funny side of marriage. These funny marriage quotes are good stress busters. They make you laugh at the banalities of marriage. When you read funny marriage quotes, you realize that even a perfect marriage has its inherent flaws but those flaws add to the charm of marriage. Funny Marriage Quotes Ogden Nash: To keep your marriage brimming, with love in the loving cup, whenever youre wrong admit it; whenever youre right shut up. Bill Cosby: For two people in a marriage to live together day after day is unquestionably the one miracle the Vatican has overlooked. Patrick Murray: Ive had bad luck with both my wives. The first one left me and the second one didnt. Gloria Steinem: I have yet to hear a man ask for advice on how to combine marriage and a career. Groucho Marx: Some people claim that marriage interferes with romance. Theres no doubt about it. Anytime you have a romance, your wife is bound to interfere. Agatha Christie: An archaeologist is best husband a woman can have: the older she gets, the more interested he is in her. Milton Berle: A good wife always forgives her husband when shes wrong. Zsa Zsa Gabor: A man is incomplete until he is married. After that, he is finished. Henry Youngman: Some people ask the secret of our long marriage. We take time to go to a restaurant two times a week. A little candlelight, dinner, soft music and dancing†¦ she goes Tuesdays, I go Fridays. Joyce Brothers: My husband and I have never considered divorce... murder sometimes, but never divorce. Homer: There is nothing nobler or more admirable than when two people who see eye-to-eye keep house as man and wife, confounding their enemies and delighting their friends. Rodney Dangerfield: My wife and I were happy for 20 years†¦ then we met. Rita Rudner: I think men who have a pierced ear are better prepared for marriage. Theyve experienced pain and bought jewelry. Ogden Nash: Marriage is the alliance of two people, one of whom never remembers birthdays and the other who never forgets. Lord Byron: All tragedies are finished by a death, all comedies by a marriage. Phyllis Diller: Whatever you may look like, marry a man your own age - as your beauty fades, so will his eyesight. Katharine Hepburn: If you want to sacrifice the admiration of many men for the criticism of one, go ahead†¦ get married. Joyce Brothers: Marriage is not just spiritual communion; it is also remembering to take out the trash. George Lichtenberg: Love is blind, but marriage restores its sight.