# IAS: Sets

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Define elementary theory of sets, also explain various methods by giving suitable examples, narrate the utility of set theory in an organization.

a set is a collection of items, objects or elements, which are governed by a rule indicating weather an object belong to the set or not. In conventional notation of sets.

Alphabets like A, B, C, X, U; S etc are used to denote sets. Braces like ‘curved ones’ are used as a notation for collection of objects or elements in the set. Greek letter epsilon is used to denote belongs to. A vertical line is used to denote expression ‘such that’ Alphabet ‘I’ is used to denote an ‘integer’ Using above notation a set called a considering of elements 0, 1, 2,3, 4,5 May be mathematically denoted in any of the following manner

List or roster method: This means all elements are actually listed. A = (0, 1, 2,3, 4,5) read as A is a set with elements 0, 1, 2,3, 4,5

set builder or rule method in which a mathematical rules, equality or in equality etc are specified to generate the elements of intended set, A = (x vertical line 0 < x < 5) , where (I = 1, 2,3, 4,5) . Read as A is a set of (variable x) such that (x lies between 0 and 5, both inclusive) where variable x belongs to integers.

Universal set is a set consisting of all objects or elements. Is a set consisting of all objects or elements of a type or a given interest and is normally depicted by alphabets X, U or S.

For example, A is set of all digits may be expressed as X = (0, 1, 2, 3, 4, 5, 6,7, 8,9)

Finite set is one in which the number of elements can be counted. For example, A = (1,2, 3,15) having 15 elements Or a set of employees in an organization.

Infinite set is one in which the number of elements cannot be counted. For example, a set of integers or real numbers.

Subset a is called a subset of B if every elements of a is also an element of B. This is represented as A B and is read as A is a sub set of B. For example, each of sets A = (0, 1, 2,3, 4,5) OR THE SET B = (1,3, 5) are subset of set C. WHERE C = (0, 1, 2,3, 4,5)

Supersets A IS a superset of B, if every element of b is an element of B. This represents as A B and read as A is superset of B.

Equal sets if A is sub set of B and B is a subset of A then A and B are called equal sets. This can be denoted as follows: If A B and B A then A = B

## Utility of Set Theory

A company consists of sets of resources like personnel, machines, material stocks and cash reserves. The relationship between these sets and between the subsets of each set is used to equate assets of one kind with another. The subsets of highly skilled production workers, within the sets of all production workers, are critical subset that determines the productivity or other personnel. Certain subsets of company products are highly profitable or certain material may be subject to deterioration and must be stocked in greater quantities than others. Thus the concept of sets is very useful in business management.

explain the meaning and type of data as applicable in any business. How would you classify and tabulate the data, support your answer with example.

data is any group of observation or measurement related to the area of a business interest and to be used for decision making. It can be of the following two types.

- Qualitative data (representing non numeric feature or qualities of object under reference)
- Quantitative data (that represent properties of object under reference with numeric details)

### Types of Data

Data can also be of the following types:

- Primary data (are observed and recorded as apart of an original experiment or survey)
- Secondary data: (are compiled by someone other than the user of the data for decision making purpose)

## Classification and Tabulation of Data

Data can be classified by geographical areas; chronicle sequences; qualitative attributes like urban or rural, male or female, literate or illiterates, under graduate, graduate or post graduate, employed or unemployed and so on; while the most frequently used method of classification of data is the quantitative classification.

## Tabulation

After data is classified it is represented in a tabular form. A self explanatory and comprehensive table has a table number, title of the table, caption (column or sub-column headings) , stubs, body containing the main data which occupies the cells of the table after the data has been classified under various caption and stubs. Head notes are added at the top of the table for general information regarding the relevance of the table or for cross reference or links with other literature. Foot notes are appended for clarification, explanation or as additional comments on any of the cells in the table.