Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.1

2.1 SET THEORY

In our daily life we use phrases like a bunch of keys, a set of books, a tea set, a pack of cards, a team of

players, a class of students, etc. Here the words bunch, set, pack, team, class – all indicate collections of

aggregates. In mathematics also we deal with collections.

A set is a well-defined collection of distinct objects. Each object is said to be an element (or member) of

the set.

The symbol ∈ is used to denote ‘is an element of’ or is a member of’ or ‘belongs to’. Thus for x ∈A. read as

x is an element of A or x belongs to A. Again for denoting ‘not element of’ or ‘does not belongs to’ we put

a diagonal line through ∈ thus ∈/. So if y does not belong to A, we may write (using the above symbol), y

∈/A

e.g. If V is the set of all vowels, we can say e ∈ V and f ∈/ V

Methods of Describing a Set.

There are two methods :

1. Tabular Method (or Roster Method)


2. Selector Method (or Rule Method or Set Builder Method)
   Tabular Method or Roster Method :
   A set is denoted by capital letter, i.e. A, B, X, Y, P, Q, etc. The general way of designing a set is writing all the
   elements (or members) within brackets ( )or { } or [ ]. Thus a set may be written again as A = { blue, green,
   red}. The order of listing is not important. Further any element may be repeated any number of times
   without disturbing the set. The same set A can be taken as A = {blue, green, red, red, red}.
   Selector Method (or Rule Method or Set Builder Method) :
   In this method, if all the elements of a set possess some common property, which distinguishes the same
   elements from other non-elements, then that property may be used to designate the set. For example, if x
   (an element of a set B) has the property having odd positive integer such that 3 is less than equal to x and
   x is less than equal to 17, then in short, we may write,
   B = {x : x is an odd positive integer and 3 ≤ x ≤17}

Study Note - 2

ALGEBRA

This Study Note includes

2.1 Set Theory

2.2 Inequations

2.3 Variation

2.4 Logarithm

2.5 Laws of Indices

2.6 Permutation & Combination

2.7 Simultaneous Linear Equations

2.8 Matrices & Determinants