Definition of SETS, Union, Intersection and Complement Benjamin Quarshie Section A Assignment Information Set Theory Explain the following terms: Â Â SETS The word set is generally associated with the idea of grouping objects, such as a set of records, books, crop plants and other words such as herd, herd, herd, plots, peasantry, family, etc. Saying the word set denotes a collection of elements clearly between them, which keep some characteristic in common. Be it numbers, people, figures, ideas and concepts. In math, the concept of a set is considered primitive and does not give a definition of it, but rather works with the notation of collection and grouping of objects, so it may be said that the ideas of element and belonging are considered primitive. The essential characteristic of a set is to be well defined, i.e. given a particular object, to determine whether or not it belongs to the set. For example, if we consider the set of digit numbers, we know that 3 belong to the set, but 19 do not. On the other hand the set of beautiful musical works is not a well defined set, since different people can include different works in the set. Objects that form a set are called members or elements. For example the set of letters of alphabet; A b c x, y, z which can be written like this: Example of two sets, A and B: UNION The union of sets corresponds to the unification of the elements of two conjuncts or even more sets, which may from this constitute a new form of set, in which the elements within it correspond to the elements of the original sets. When an element is repeated, it forms part of the union set once only; This differs from the union of sets in the traditional conception of addition, in which common elements are considered as many times as they are in the totality of sets. We can say that the union of sets is a binary operation (that mathematical operation, which requires the operator and two arguments to be able to calculate a value) in the set of all subsets of a U, Universal Set consisting of all elements of the reference theme) given. By which each pair of sets A and B of U is associated with another set (A U B) of U. If A and B are two sets, the union is defined as follows: INTERSECTION The Intersection of two or more sets is the set formed by the elements that have in common both sets. The intersection of A and B is denoted. In diagrams all the elements in their respective sets are first represented and then the zone belonging to both sets is coloured. COMPLEMENT The complement of a complementary set or set is another set that contains all elements that are not in the original set. In order to define it, it is necessary to specify what type of elements are being used, or otherwise, what the universal set is. For example, if one speaks of natural numbers, the complement of the set of prime numbers P is the set of non-prime numbers C, which is composed of the compound numbers and the 1: UNIVERSAL SET This is called the set that contains all the elements. This set depends on the problem being studied, is a set whose object of study are the subsets of it. Primarily the universal whole was considered as the set of all things, but at present it is proved that this set does not exist. At the present time it should be made clear which set is being treated. If we treat sets whose elements are letters, the universal set would be the one that was formed by all the letters of the alphabet. The complement of the universe (or referential) set is the empty set. The universal set is indicated by the letter U and sometimes indicated by the letter S. POWER SET 2.5 Venn Diagrams SET A (EVEN NUMBERS)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SET B (NUMBERS DIVISIBLE BY 5) Show the 2 sets using bracket notation SET A = {2,4,6,8,10,12,14,16,18,20} SET B = {5,10,15,20,25,30} 2.2 The union of set A and set B are listed below: Â Â Â Â Â Â Â Â Â Â A U B = {2,4,5,6,8,10,12,14,15,16,18,20,25,30} 2.2 The intersection of Set A and Set B A n B = {30,8,2,10,14,25} 2.3 The Complement of Set A d) D is the set of dogs which includes the following subsets B (the set of Boxers), L (the set of Labradors) and P (the set of Poodles). Express the power set of D using bracket notation. SET B SET P SET L References Webpage [http://study.com/academy/lesson/union-of-sets-in-math-definition-terms-symbol.html] Accessed on [24/02/2017] Webpage [https://www.reference.com/math/well-defined-set-mathematics-4895437ff1cbabd9] Accessed on [24/02/2017] Webpage [http://searchsecurity.techtarget.com/definition/set] Accessed on [27/02/2017]
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Moreover, Tom had to look for sponsors to fund the advertising and campaigning costs. The national environmental protection agency donated 300,000 United States dollars to assist in creating public awareness about the bill and urge more people to vote for it (Ragsdale 137-138). A linear programming (LP) spreadsheet model would play a significant role in designing how to allocate the provided funds to different advertising agents. The spreadsheet model assists in determining the total impact of using various advertising agents, the total constraints, and the optimal solution. Description of the data The data from the spreadsheet consists of 3 columns. The first column C shows the cost per unit of the advertising medium used in U.S. dollars. The following data represents the objective variables. The objective variables work in maximizing or minimizing numerical values. The value presented on the objective cell is the expected net budget value of the project. The product of C and decision units I give the total cost of advertisement. The second set of data is represented by E showing per unit impact rate. This column represents the constraints. Constraints define any possible variable that a linear programming problem takes. In the data E provided, constraints represent percentage impact of using a certain medium for advertising. The next data is represented by G showing the minimum value of decisions made with the smallest advertising medium. On the other hand, column K presents data of the maximum decision a product of using large advertising mediums. Discuss the results After constructing the spreadsheet and doing calculations, the following results were arrived at. What is the optimal solution? The total impact rate was $23,515. The values for impact rate were arrived at by multiplying E with I. The total impact rate was used to calculate the optimal solution in order to decide which advertising medium would be more effective. From the model, the optimal solution was arrived at by the following calculation. X = 300,000/A (1+2+3+4+….n) + B (1+2+3+4…n) =300,000/ (299,800 + 23,515) = 0.927 The following results indicate that 92.7% of the total budget would be well utilized by the advertising mediums proposed by Tom. The following turn out is very pleasing and Tom was likely to receive many votes towards the policy. Of the constraints tom placed on this problem, which are preventing the objective function from being improved further? On the other hand, Tom placed some constraints that prevented further improvement the objective function. The objective function on full-page Sunday paper and 30-second radio spot are in significant because they cost a lot and serve the same purposes as the half-page Sunday magazine and 15-second radio spot respectively. In addition, long magazine advertisements are sometimes boring and time consuming and most people by pass them. The absence of such constraints would give Tom an opportunity to incorporate other advertising mediums like online ads. The marketing consultant provided short TV ads during the evening prime-time hours as the most effective medium of advertising. Suppose Tom was willing to increase the allowable number of evening TV ads. How much would this improve the solution? Improving the number of evening TV ads would cause a positive effect on the advertisement and increase the value of $23,515 into a higher level. Increased evening TV ads increases the impact rate since a high number of |