Definition and Usage of Union in Mathematics

One operation that is frequently used to form new sets from old ones is called the union. In common usage, the word union signifies a bringing together, such as unions in organized labor or the State of the Union address that the U.S. President makes before a joint session of Congress. In the mathematical sense, the union of two sets retains this idea of bringing together. More precisely, the union of two sets A and B is the set of all elements x such that x is an element of the set A or x is an element of the set B. The word that signifies that we are using a union is the word or. The Word Or When we use the word or in day-to-day conversations, we may not realize that this word is being used in two different ways. The way is usually inferred from the context of the conversation. If you were asked â€Å"Would you like the chicken or the steak?† the usual implication is that you may have one or the other, but not both. Contrast this with the question, â€Å"Would you like butter or sour cream on your baked potato?† Here or is used in the inclusive sense in that you could choose only butter, only sour cream, or both butter and sour cream. In mathematics, the word or is used in the inclusive sense. So the statement, x is an element of A or an element of B means that one of the three is possible: x is an element of just A and not an element of Bx is an element of just B and not an element of A.x is an element of both A and B. (We could also say that x is an element of the intersection of A and B Example For an example of how the union of two sets forms a new set, let’s consider the sets A {1, 2, 3, 4, 5} and B {3, 4, 5, 6, 7, 8}. To find the union of these two sets, we simply list every element that we see, being careful not to duplicate any elements. The numbers 1, 2, 3, 4, 5, 6, 7, 8 are in either one set or the other, therefore the union of A and B is {1, 2, 3, 4, 5, 6, 7, 8 }. Notation for Union In addition to understanding the concepts concerning set theory operations, it is important to be able to read symbols used to denote these operations. The symbol used for the union of the two sets A and B is given by A ∠ª B. One way to remember the symbol ∠ª refers to union is to notice its resemblance to a capital U, which is short for the word â€Å"union.† Be careful, because the symbol for union is very similar to the symbol for intersection. One is obtained from the other by a vertical flip. To see this notation in action, refer back the above example. Here we had the sets A {1, 2, 3, 4, 5} and B {3, 4, 5, 6, 7, 8}. So we would write the set equation A ∠ª B {1, 2, 3, 4, 5, 6, 7, 8 }. Union With the Empty Set One basic identity that involves the union shows us what happens when we take the union of any set with the empty set, denoted by #8709. The empty set is the set with no elements. So joining this to any other set will have no effect. In other words, the union of any set with the empty set will give us the original set back This identity becomes even more compact with the use of our notation. We have the identity: A ∠ª ∅ A. Union With the Universal Set For the other extreme, what happens when we examine the union of a set with the universal set? Since the universal set contains every element, we cannot add anything else to this. So the union or any set with the universal set is the universal set. Again our notation helps us to express this identity in a more compact format. For any set A and the universal set U, A ∠ª U U. Other Identities Involving the Union There are many more set identities that involve the use of the union operation. Of course, its always good to practice using the language of set theory. A few of the more important are stated below. For all sets A, and B and D we have: Reflexive Property: A ∠ª A ACommutative Property: A ∠ª B B ∠ª AAssociative Property: (A ∠ª B) ∠ª D A ∠ª (B ∠ª D)DeMorgan’s Law I: (A ∠© B)C AC ∠ª BCDeMorgan’s Law II: (A ∠ª B)C AC ∠© BC

My Philosophy of Education Essay - 1211 Words

Philosophy of Education According to Webster’s Dictionary, â€Å"A teacher is a person who teaches especially for a living.† This definition though is not entirely true about a teacher. As a teacher not only do you teach students, but teachers are parents, social workers, nurses, and even friends. A good teacher should be able to play all of these roles and will be successful throughout their teaching career. I attended public schools, so I got the good, the bad, and the ugly of every kind of teacher one could possibly have. The good teachers I had throughout school are what inspired me to become a teacher now. I am pursing a major in mathematics even though a lot of people think I am crazy for doing so, but the school†¦show more content†¦As a teacher I hope to accomplish many things. I hope to have my students go on and remember me for years. I hope to remember my students for years as well and the lessons they teach me. I want my students to want to learn mathematics and be good a t. I know my students will come in and know that I am in charge, but their opinions and thoughts do matter. I wish that when my students finish my course for the year that they know the material that I have gone over and that they want to learn more math. There are so many students that I hear that hate math, I want to change that. I want all of my students to love math and want to learn it. This might sound like high standards, but I am going to make it happen. Overall, even if my students don’t make straight A’s or even B’s, if they are struggling I want to be able to teach them so that the do pass. Another note is that they accomplish more and do better in math than they have ever done. My classroom will have discipline and the students are going to know who is in charge. I don’t agree with the classrooms where it is like a dictatorship and everything the teacher says goes. I want my students to make up the rules at the beginning of the year and I will modify them to fit the classroom. I know not at all times students are going to follow the rules because I remember back in middle and high school when it was Friday most students were ready for the weekend. The rulesShow MoreRelatedMy Philosophy On The Philosophy Of Education844 Words   |  4 PagesIn mathematics, as in life, everything must be brought to the simplest of terms. I base my teaching philosophy on the foundation that every student is capable of learning mathematics. I will strive, as a teacher, to ensure that my students are able to have a strong foundation of mathematical skills when they leave my classroom. Some students believe that they are not mathematically gifted; therefore, i ncapable of learning mathematics. I believe to the contrary, all students with motivation, sustainedRead MoreMy Philosophy On Philosophy Of Education852 Words   |  4 PagesMy Philosophy of Education My philosophy of education is founded on a belief that all students have a desire to learn and to feel accepted. Learning takes place when students are able to have their specific needs meet inside the classroom, to feel accepted in the environment, and find the learning to be meaningful. I believe that before learning can take place a proper educational environment must be present inside the classroom. In order to make any classroom work I believe you need meet three criteriaRead MoreMy Philosophy Of Education As A Education864 Words   |  4 Pagesdifferent philosophy of education, and what purpose education serves in a child’s life. The five philosophies of education that we recognize are: Essentialism, Perennialism, Progressivism, Social Reconstructionism, and Existentialism. 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But when you decide to become a teacher in a Christian school you are not only shaping this student to be successful in life but we are also shaping their Christian mind to do things with a feeling knowing that they are shape and where made by the image of GodRead MoreMy Philosophy Of Education1015 Words   |  5 Pagesimmediately sparked my interest in becoming an educator and share my personal beliefs on the important aspects of education. In addition to this, I will present various traits I believe are essential and critical for teachers to successfully fulfill their role as an educator. During my elementary years, I developed an urge to frequently ask many questions during the school day. Being able to question anything was astonishing to me. This was because my parents were unable to answer my questions and help

Most Effective Kicks in Tae Kwon-Do Free Essays

Some kicks are more useful than others, so I’ll be walking you through the most powerful/effective kicks that are In Ate Swoon-Do. Let’s go through the attributes of a kick, we’ll start off with the base leg, the leg that stays on the ground during the kick. This leg Is just as Important (If anything more important) than you’re kicking leg, due to the fact that this leg has to grant you the flexibility to initiate the kick and also has to maintain balance throughout the kick. We will write a custom essay sample on Most Effective Kicks in Tae Kwon-Do or any similar topic only for you Order Now Whenever you begin a kick, you should allow the heel of the foot of your base leg to e raised slightly upward (Thus resting on the ball of your foot) to maintain maximum mobility while the kick is in motion, allowing you to turn in the correct position for the kick. If you need to shift your position as your Initiating the kick. You can also slide/ skip on the ball of your foot toward the desired direction. The knee of your base leg should be slightly bent whenever you perform a kicking technique, this adds to the over-all balance of your body; you will be able to adjust your position easily, by adding more or less bend to your knee, to compensate for the height and velocity of our kick. Now onto the striking leg, first off you never really want to fully extend your leg when kicking. The knee of the striking leg should remain slightly bent. This is accomplished by maintaining muscle control over the lower part of your leg, and not allowing the momentum of the kick to force your leg to hyper extend. Because the knee joint is one of the most sensitive joints of the human body be sure to keep both knees slightly bent, to prevent them hypertension or bending backward unnaturally. Side Snap The basic side snap, is performed by initially shifting the majority of your body eight to your base leg as your striking leg (Be it your front or rear leg) rises up with a bent knee to waist level. As your striking leg rises, you pivot on the ball of your base foot so your heel is facing your target. Your body leans sideways toward the ground as your striking leg is extended toward your target. The impact is made with the heel or outside ridge of your foot. You can substantially Increase the range of the side snap by allowing the momentum of its launch to drive you forward. To do so, enter into a fighting stance and begin by launching the side snap with the front or rear leg. Round. By performing the side snap in this fashion, you allow your base leg to slide slightly forward across the floor, propelled by the momentum developed when your striking leg is launched toward its target. Not only does this add to the range of the kick, but also increases its power as well, due to the fact that the force of your entire body is behind it. One of the main problems with delivering the sliding side snap is that many people will release the kicks power before they are in range of their target. When performing the side snap in this style, it is imperative to remember not to unleash your striking legs power from your hip, until your target is close and you are sure of making contact with it. If this kick is done to far from your target, the most you can hope to accomplish is that your extended leg will make touching contact with your opponent. You will not, however, have any debilitating impact. Therefore, keep your side snap retracted until target impact is ensured. Turn-around Side Snap Structurally similar to the side snap, the turn-around side snap is a spinning variation of the basic side snap. This kick is executed by first turning your head round, keeping an eye on your target. You turn your head simultaneously pivoting your body on the ball of the foot of you lead base leg so that the heel of your base leg is facing your opponent. Your kicking technique is then launched from rear-leg position, in side kick fashion The turn-around side snap is a muscle-driven technique. Impact with this kick is made with the heel or the outside ridge of your foot. The ideal targets for the turn-around side snap are your opponent’s knee, midsection or head The turn-around side snap can be used both offensively and offensively; it can be used as a single offensive movement or as a rapid combination of kicks alternating from one foot to the next. It can also be used defensively as a counter attack when your opponent is throwing a punch or a kick that leaves him open. All-Around Swing Kick The all-around swing kick is one of the most powerful techniques in a Ate Swoon- Do practitioner’s kicking arsenal. The momentum this kick can have has a devastating effect upon any object it strikes. The all-around swing kick is executed by turning your head around behind you, to make sure your target hasn’t moved, as you multitudinously pivot 1800 on the ball of your base foot. Your rear leg lifts off the ground and proceeds toward its target in a circular fashion. This kick strikes its target with the back of your heel. The all-around swing kick is most effective when delivered to the head or mid-section of your opponent. It is important to drive your kick to go â€Å"through† your target, in other words, you don’t want to stop Just as you hit your target, you want the kick to follow through. Doing this well result in greater power and making it harder to defend against. Like most kicks, the all-around swing kick can be used defensively or offensively Front Snap The front snap, is one of the first kicks that all Ate Swoon-Do students learn. Most devastatingly effective offensive/defensive techniques in your kicking arsenal when performed correctly. The basic front snap is performed by entering into a traditional fighting stance. You then launch your striking leg forward by quickly raising the knee of your striking leg up to the desired height (It all depends on where you planning to attack, be it the head, mid-section or legs). The lower section of your tricking leg is then immediately snapped outward in the direction of your target. The front snaps power is developed by a combination of upper-leg muscle strength and lower-leg snapping momentum. The impact of the kick can be made with either the instep of your foot of the ball of your foot. To strike with the ball of your foot, you need to pull back your toes, exposing the ball of your foot. Performing the front snap with the ball of your foot is more advanced and takes additional practice. Through continued practice, however, the ability to instantly pull back your toes will become tie natural. The reason it is so important to pull back your toes (Even if you are wearing shoes), is that if you leave them in their naturally extended position, they can easily be broken when target impact is made. The basic front snap is an ideal close- contact fighting weapon. As us commonly understood, a front snap to the groin of any individual is universally debilitating. Other close-contact targets for this kick include; the solar plexus, the stomach, or the bottom of your opponent’s Jaw. Axe Kick The axe kick, is a close-contact offensive and defensive weapon. The axe kick is performed by quickly raising your striking leg (Depending if your kicking with your front or rear leg), in a linear fashion, and then forcefully bringing your heel/ball of your foot, down onto the shoulder/chest/face of your opponent. The basic axe kick is only effective in close-contact infighting situations, but it is quite easy to extend the range of this kick. Enter into a fighting stance and prepare to launch an axe kick from your preferred leg front of rear (although it’s mainly used with the rear leg). Now instead of performing it with your leg locked into position, visualize a target several feet in front of you. Quickly lift your striking leg. As you target. There are two ways to execute an axe kick; the traditional axe kick is brought inward, across your body, and then down-ward onto its target. The out-to-in axe kick is swung outward and is then brought down onto you opponents shoulder. The out-to-in axe kick is also a close- contact infighting weapon. It can most effectively be dispatched when your attacker has been taken hold of your clothing, or you have hold on his. Then, like before, the kick is quickly brought up and delivered to your opponents shoulder region Conclusion As we can see, kicks play a huge part in Ate Swoon-Do, we only went through 4 different kicks, there are many other (Such as hook kick, turning kick, swing kick, crescent kick, all-around hook kick, all-around swing kick†¦ Etc,). Kicks don’t need to be complicated or hard to perform in order to be effective, like we went through at the start, for a kick to be effective in combat, it needs to be fast, difficult to block and able to get through you’re opponents guard and hit its target. How to cite Most Effective Kicks in Tae Kwon-Do, Papers

Essay on Junk Food By Judith Warner Essay Example For Students

Essay on Junk Food By Judith Warner Essay The essay Junking Junk Food by Judith Warner, brings to the audience s attention the wicked problem of how there has been a decline in Americans health. Warner’s information speaks loudly about the effects of the government trying to limit types and amount of food we consume as a nation. The Obama administration tried to enforce a healthy lifestyle among the citizens by focusing on the youth and taking away sugar options for them. These efforts by the administration are being mocked by Warner because without the government controlling what we eat, we cannot make the proper decisions ourselves. Majority of Americans today are either obese or overweight and the best way to change Americans is by attitudes and culturally. The 78 million adults and 13 million children in America who are obese are at risk for health and financial problems. While we continue to be more aware of this health issue, we still have few ideas to correct it. According to Warner the one of the most successful examples in time of food rationing by the government was during World War World War II. This time it will take more than that to cut down on consumers intake. Obesity is a fast growing disease that spread widely across America that is a result of incompetency, convenience and financial situations. Blaming incompetency may seem strange, but with obesity rates growing at eye opening rate you can assume over consuming is occurring. While this is occurring many Americans lack nutritional information on their food and not only if it is missing, it is very difficult to understand or find. It is easy to state that it is difficult to find serving sizes and ingredients especially at fast food restaurants. While salads are the healthier option they seemly can be . .rner’s essay, â€Å"Junking Junk Food† connects to Zinczenko’s â€Å"Don’t Blame The Eater† in both addressing the topic of obesity. Where it is not the responsibility of the consumers. Fast food is very unhealthy has lack of nutritious components and value but is ready quick, and from there on that s when the consumer must learn to make the good choice for themselves. Though, for majority of Americans the role of incompetency, convenience and financial state comes into play when making the unhealthy food choice, but it must end somewhere. Healthy food must be made more available, affordable and quick. As Warner says the people must understand that the difference can be made by changing attitudes, culture, and habits. This will not be easy and will take time but then there will be no excuse for consumers to make anymore and will put an end to the fast growing obesity disease.

Auditing And Assurance Handbook Australia â€Myassignmenthelp.Com

Question: Discuss About The Auditing And Assurance Handbook Australia? Answer: Introducation The requirement of Ethics is perhaps universal but one profession where ethical conduct is perhaps more critical than the others is the accounting profession considering the role that user trust plays in continued relevance of this profession (Arens et. al., 2013). Unethical conduct on the part of the accounting professions can violate the trust of the investors and other users such as lenders and creditors and thus reduce the need for reporting and also auditing. As a result, for accounting professionals various codes of conduct have been established which highlight the model qualities they need to display in their conduct (Cheffers Pakaluk, 2007). One of the most prominent ones in Australian context is APES 110 which has been released by APESB (Accounting Professional and Ethical Standards Board). In view of the above background, the objective is to highlight how APES 110 promotes ethical conduct and thus greater trust from the public which is considered imperative for the profess ion especially in the present challenging environment. It is evident that trust essentially is linked to ethical behaviour on the part of accountants. As a result, the crucial question arises as to the meaning of ethical conduct in the accounting field. One of the theories of ethics named as virtue ethics provides hint in this regards by highlighting key desirable virtues for accountants as courage, wisdom, justice and mastery. The justice in the accounting profession implies that the accountant would use the available knowledge and skills to ensure that a fair representation of the financial statements must be brought forward (Cheffers Pakaluk, 2007). This is supported by the APES 110 through the insertion of section 120 which tend to deal with objectivity. The section on objectivity requires the accounting professional to be objective with regards to the professional judgement application which would involve questioning the key assumptions made by the client and verify the accuracy of the same. Also, this demands that irrespective of the situation, there should not be any impairment in this objective. The situations which compromise these have also been highlighted which involve conflict of interest or in the presence of undue influence (APESB, 2010). Further, courage essentially refers to the use of available skillsets in a manner that tends to serve the informational needs of the external users. This would involve detection of any frauds and also ensuring that there are no mistakes when the accounting or audit work is taking place (Cheffers Pakaluk, 2007).. This is highlighted in section 130 of the APES 110 code which tends to deal with professional competence and due care. As per this objective, it is necessary that the professionals must regularly update their knowledge and skillsets so that the information needs of the client are met (APESB, 2010). Possession of skills and regular updating has special significance for the accounting field considering that the accounting standards are inherently dynamic and also the type of instruments used by companies for financing are also undergoing rapid change and increasing complexity which poses a challenge for the professionals (Caanz, 2016). However, with requisite and updated techn ical knowledge coupled with due care, the accountants can ensure that the informational needs of the users are satisfied in a reliable manner (Gay Simnett, 2012). The next desirable virtue is wisdom which essentially relates to not only available skills but applying them with due care and professionalism (Cheffers Pakaluk, 2007). This is captured by the APES 110 in the form of section 150 which deals with professional behaviour. Hence, it is imperative that the accounting professional must adhere to the various laws and obligations while conducting their work and should not do anything that would discredit the profession (APESB, 2010). Thus, when the accounting professionals make a particular representation to the client, they should be wise enough so view the implications of their actions over the long term which could be potentially disastrous. The last of the desirable virtues which is especially relevant in the current times is self mastery. This is because offlate there have been numerous high profile bankruptcy cases where the contribution of the auditor to the bankruptcy was found to be significant (Cheffers Pakaluk, 2007) . It is ess ential that the independence of the accounting professional should be maintained so that no quid pro quo relation is established with the management (Leung, Coram Cooper, 2012). This is ensured through insertion of section 110 which deals with integrity and is considered the biggest contributor to public trust. The section 110 puts the obligation on the accountants and auditors to be honest in their professional dealings and should not be a part of any initiative which can potentially misguide or mislead the intended users. Hence, this section highlights the emphasis of honest conduct for the accountants conduct (APESB, 2010). The use of APES 110 is relevant from the perspective of increasing trust as it highlights the various threats to independence and also suggests the various mechanisms to ensure that these threats are addressed in the requisite manner. This is essential considering that the trust of people on accountants is dwindling and the primary reason for the same is compromised independence (Arens et. al., 2013).. However, the APES 110 highlights the various situations in which independence may be compromised knowingly or unknowingly. For instance, the accepting gift from client which the client may try to justify as a goodwill gesture is not permitted under this standard (Cheffers Pakaluk, 2007). This is quite useful as the APES 110 considers both actual independence and perceived independence and gives prescribes conduct to safeguard both these. This is imperative especially for a profession which has low trust ratings from users as any perception by the users in relation to independence bein g compromised could be pivotal irrespective whether this has happened or not in actual (Caanz, 2016). Also, various situations which can lead to conflict of interests have been outlined so as to guide the accounting professions on the nature of situations that should be avoided and the code also offers the conduct expected if the accounting professional is caught in such a situation. The list of potential situations is quite exhaustive and tends to cover the common situations that could arise (Gay Simnett, 2012). Thus, APES 110 acts as a useful guide which is coming from an authentic source and can enable ethical decision making on the part of the professionals in relation to the decisions they are expected to make which at times involve ethical dilemma. The priority of interest in this regard is also critical as misreporting at times may help the employees and an honest promoter but the supreme responsibility of the accounting professional should be towards the intended users and the profession and hence ethical conduct must not be compromised for any reason and situation (Leung, C oram Cooper, 2012) The safeguards which are highlighted for the various situations are also pivotal as it enables improvement in the corporate governance of both the firms offering auditing and accounting services along with their clients. This in turn would enable that there is lowering of opportunity to act in a fraudulent manner for the professions which is also essential in order to build trust. Hence, on the side of the firm offering services, the APES 110 expects that there should be ethics training and awareness provided to the professionals besides having reasonable checks and balances in the form of control mechanisms (Arens et. al., 2013). On the side of the client, The APES 110 highlights the appropriate conduct to be directed against accounting and auditing professions so that their independence is not adversely impacted and a cordial professional relationship can be maintained based on mutual trust and respect. Also, there is a dedicated section 240 which pertains to the ethical conduct in relation to remuneration (Caanz, 2016). Typically in cases of frauds, it has been seen that there is high audit fees being paid coupled with lucrative consulting contracts. Conduct in relation to charging the various fees has been outlined which provides clarity to the professionals, firms and clients. Additionally, in relation to the collection of overdue also, proper mechanism has been laid out. These communicate the model behaviour to be adopted and thus provide guidance to conduct of professionals which in turn would prevent fraudulent or unethical conduct (Cheffers Pakaluk, 2007). On account of the above discussion, it may be concluded that indeed APES 110 is a useful tool in order to promote and improve the ethical conduct of the accounting professions. This is achieved through guidance offered by APES 110 on a host of matters. The first one relates to highlighting the key characteristics to be safeguarded which in turn upheld the virtues expected from the professionals in this area. Additionally, it also mentions the various threats to the auditor independence which adversely impacts the trust of the users. Further, it also provides safeguards which ought to be implemented at various levels in order to ensure that auditor independence remains intact. Besides, specific guidance is also offered to the professionals and the firm regarding conduct in various situations so that the user trust is upheld. Hence, APES 110 is a useful tool in relation to improving the trust of public in the accounting profession. References APESB (2010), APESB 110 Code of Ethics for Professional Accountants, APESB Website, Retrieved on September 18, 2017 from https://www.apesb.org.au/uploads/standards/apesb_standards/standardc1.pdf Arens, A., Best, P., Shailer, G. Fiedler,I. (2013). Auditing, Assurance Services and Ethics in Australia (2nd ed.), Sydney: Pearson Australia Caanz, S. (2016), Auditing and Assurance Handbook 2016 Australia (3rd ed.), Sydney: John Wiley Sons Cheffers, M. Pakaluk, M. (2007), Understanding Accounting Ethics (2nd ed.), Sydney: Allen David Press Gay, G. Simnett, R. (2012), Auditing and Assurance Services in Australia (5th ed.), Sydney: McGraw-Hill Education Leung, P., Coram, P. Cooper, B.J. (2012), Modern Auditing and Assurance Services (4th ed.), New York: John Wiley Sons

The Iran-Contra Affair Essays - IranContra Affair,

The Iran-Contra Affair The tangled U.S. foreign-policy scandal known as the Iran-contra affair came to light in November 1986 when President Ronald Reagan said yes to reports that the United States had secretly sold arms to Iran. He said that the goal was to improve relations with Iran, not to get releases of U.S. hostages held in the Middle East by terrorists (although he later agreed that the arrangement had in fact turned into an arms-for-hostages swap). People spoke out against dealings with the hostile Iranian government all over the place. Later in November, Att. Gen. Edwin Meese discovered that some of the arms profits had been used to aid the Nicaraguan "contra" rebels at a time when Congress had prohibited such aid. An Independent special prosecutor, former federal judge Lawrence E. Walsh, wa appointed to investigate the activities of persons involved in the arms sale or contra aid or both, including marine Lt. Col. Oliver North of the National Security Council (NSC) staff. Reagan appointed a review board headed by former Republican senator John Tower. The Tower commission's report in February 1987 criticized the president's passive management style. In a nationaly televised address on March 4, Reagan accepted the reports judgement without serious disagreement. Select committees of the Senate (11 members chaired by Democrat Daniel K. Inouye of Hawaii) and the house of representatives (15 members, headed by another Democrat, Lee Hamilton of Indiana) conducted televised hearings in partnership from May to August. They heard evidence that a few members of the NSC staff set Iran and Nicaragua policies and carried them out with secret private operatives and that the contras received only a small part of the money. Former national security advisor John Poindexter stated that he personally authorized the diversion of money and withheld that information from the president. William J. Casey, the director of the Central Intelligence Agency, who died in May 1989, was implicated in some testimony. His testomony still remained in doubt. Clearly however, the strange events shook the nation's faith in President Reagan and ruined U. S. prestige abroad. Special prosecutor Walsh continued his investigation. On March 11, 1988 Poindexter's forerunner as national security advisor Robert McFarlane pleaded guilty to criminal charges of witholding information from Congress on secret aid to the contras. A year later, Peter McFariane was fined $20,000 and given two years probation. On March 16, 1988, a federal grand jury indicted North, Poindexter, and two other persons on a number of charges including conspiracy to defraud the U.S. government. The trials were delayed by legal maneuvering that in part involved questions of releasing secret information. In May 1989 a jury convicted North of 3 of the 12 criminal counts he was ultimately tried on. In July the court fined North 150,000 and gave him a three- year suspended sentence. The North convictions were later set aside by a federal appeals court, which found defects in the trial procedure. On April 7, 1990, Poindexter was convicted on 5 counts of deceiving congressional investigators and sentenced to six months in prison. In July 1991, Alan D. Fiers, Jr., CIA chief of covert operations in Central America in 1984-86, admitted that he had lied to Congress and that there had been a CIA Iran-contra cover up. Shortly after, his CIA superior Clair E. George was indicted.

Top Tips for Observing Mitosis Lab

Top Tips for Observing Mitosis Lab We have all seen illustrations in textbooks of how mitosis works. While these types of diagrams are definitely beneficial for visualizing and understanding the stages of mitosis in eukaryotes and connecting them all together to describe the process of mitosis, it is still a good idea to show students how the stages actually look under a microscope in an actively dividing group of cells. Necessary Equipment for This Lab In this lab, there are some necessary equipment and supplies that would need to be purchased that go beyond what would be found in all classrooms or homes. However, most science classrooms should already have some of the necessary components of this lab and it is worth the time and investment to secure the others for this lab, as they can be used for other things beyond this lab. Onion (or Allum) root tip mitosis slides are fairly inexpensive and easily ordered from various scientific supplies companies. They can also be prepared by the teacher or students on blank slides with coverslips. However, the staining process for homemade slides are not as clean and exact as those that are ordered from a professional scientific supply company, so the visual may be somewhat lost. Microscope Tips Microscopes used in this lab do not have to be expensive or high powered. Any light microscope that can magnify at least 40x is sufficient and can be used to complete this lab. It is recommended that students are familiar with microscopes and how to use them correctly before beginning this experiment, as well as the stages of mitosis and what happens in them. This lab can also be completed in pairs or as individuals as the amount of equipment and skill level of the class allows. Alternatively, photos of onion root tip mitosis can be found and either printed onto paper or put into a slideshow presentation in which the students can do the procedure without the need for microscopes or the actual slides. However, learning to use a microscope properly is an important skill for science students to have. Background and Purpose Mitosis is constantly happening the meristems (or growth regions) of roots in plants. Mitosis occurs in four phases: prophase, metaphase, anaphase, and telophase. In this lab, you will determine the relative length of time each phase of mitosis takes in the meristem of an onion root tip on a prepared slide. This will be determined by observing the onion root tip under the microscope and counting the number of cells in each phase. You will then use mathematical equations to figure out time spent in each phase for any given cell in an onion root tip meristem. Materials Light microscope Prepared Onion Root Tip Mitosis Slide Paper Writing utensil Calculator Procedure 1.  Create a data table with the following headings across the top: Number of Cells, Percentage of all Cells, Time (min.); and the stages of mitosis down the side: Prophase, Metaphase, Anaphase, Telophase. 2.  Carefully put the slide on the microscope and focus it under low power (40x is preferred). 3.  Choose a section of the slide where you can clearly see 50-100 cells in the different stages of mitosis (each â€Å"box† you see is a different cell and the darker stained objects are chromosomes). 4.  For each cell in your sample field of view, determine whether it is in prophase, metaphase, anaphase, or telophase based on the appearance of the chromosomes and what they should be doing in that phase. 5.  Make a tally mark under the â€Å"Number of Cells† column for the correct stage of mitosis in your data table as you count your cells. 6.  Once you have finished counting and classifying all of the cells in your field of view (at least 50), calculate your numbers for â€Å"Percentage of All Cells† column by taking your counted number (from Number of Cells column) divided by the total number of cells you counted. Do this for all stages of mitosis. (Note: you will need to take your decimal you get from this calculation times 100 to make it into a percentage) 7.  Mitosis in an onion cell takes approximately 80 minutes. Use the following equation to calculate data for your â€Å"Time (min.)† column of your data table for each stage of mitosis:  (Percentage/100) x 80 8.  Clean up your lab materials as directed by your teacher and answer the analysis questions. Analysis Questions 1.  Describe how you determined which phase each cell was in. 2.  In which phase of mitosis was the number of cells the greatest? 3.  In which phase of mitosis was the number of cells the fewest? 4.  According to your data table, which phase takes the least amount of time? Why do you think that is the case? 5.  According to your data table, which phase of mitosis lasts the longest? Give reasons as to why this is true. 6.  If you were to give your slide to another lab group to have them repeat your experiment, would you end up with the same cell counts? Why or why not? 7.  What could you do to tweak this experiment in order to get more accurate data? Expansion Activities Have the class compile all of their counts into a class data set and recalculate the times. Lead a class discussion on the accuracy of data and why it is important to use large amounts of data when calculating in science experiments.