Strategies Essay Example

Strategies Essay There are many strategies that help promote changes but it is difficult to come across strategies that work on a long-term and permanent basis. Kotter’s strategy regarding the 8-stage process for organizational change works due to its ease in manageability and clearly defined goals. The first stage entitled, â€Å"establishing a sense of urgency† relates to examining the market and what would work best as well as examining the crisis as well. This ensures that there are fewer setbacks after a careful examination of the situation thereby delivering a positive culture in the state of change. The second and third stage entitled, â€Å"creating the guiding location† and â€Å"developing a vision strategy† help in clarifying the objectives and a team is gathered for a complete effort. The fourth and fifth stage entitled, â€Å"communicating the change in vision† and â€Å"empowering broad-based actions† mostly relate to inducing positive effects i n the organization by helping the team understand the essence of change and its need. The sixth stage entitled, â€Å"generating short-term wins† actually encourages the team towards rewards of any success that the organization may achieve through the change that has been incorporated by the organization. The seventh stage entitled, â€Å"consolidating gains and producing more change† is aimed at hiring personnel who can effectively work with the change thereby making the aims of the organizational change permanent and further reinvigorating the process with the new projects. The last stage entitled, â€Å"anchoring new approaches in the culture† mainly aims at supporting the changes in the organization by acting on all the above stages thereby enhancing the leadership development and succession at large. Therefore, Kotter’s eight-stage process induces a positive effect on the organizational change thereby helping the organization achieve its goals. We will write a custom essay sample on Strategies specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Strategies specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Strategies specifically for you FOR ONLY $16.38 $13.9/page Hire Writer REFERENCE: Mackinnon, Lauchlan A. K. (2007). Book Review: John Kotter on Change Management. Retrieved online on the 10th of July, 2007 at http://lauchlanmackinnon.blogspot.com/2007/06/book-review-john-kotter-on-change.html

Definition and Usage of Union in Mathematics

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