Paper 4: Fundamentals of Business Mathematics & Statistic

2.2 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

In Tabular method, B = { 3, 5, 7, 9, 11, 13, 15, 17}

Similarly, C = {x : x is a day beginning with Monday}.

[Note 1. ‘:’ used after x is to be read as ‘such that’. In some cases ‘I’ (a vertical line) is used which is also

to be read ‘such that’.

2. If the elements do not possess the common property, then this method is not applicable]
   2.1.1. TYPES OF SETS :


3. Finite Set
   It is a set consisting of finite number of elements.
   e.g. : A = {1, 2, 3, 4, 5}; B = { 2, 4, 6, ....., 50}; C = { x : x is number of student in a class}.


4. Infinite Set
   A set having an infinite number of elements is called an Infinite set.
   e.g. : A = { 1, 2, 3, .....} B = { 2, 4, 6, ......}
   C = { x : x is a number of stars in the sky}.


5. Null or empty or Void Set
   It is a set having no element in it, and is usually denoted by φ (read as phi) or { }.
   As for Example : The number of persons moving in air without any machine. A set of positive numbers
   less than zero.
   A = { x : x is a perfect square of an integer 5 < x < 8}.
   B = { x : x is a negative integer whose square is – 1}
   Remember : (i) φ ≠ {φ}, as {φ} is a set whose element is φ.
   (ii) φ ≠ {0} is a set whose element is 0.


6. Equal set
   Two sets A and B are said to be equal if all the elements of A belong to B and all the elements of B
   belongs to A i.e., if A and B have the same elements.
   As for example : A = { 1, 2, 3, 4} : B = {3, 1, 2, 4},
   or, A = {a, b, c} : B {a, a, a, c, c, b, b, b, b}.
   [Note : The order of writing the elements or repetition of elements does not change the nature of set]
   Again let A = { x : x is a letter in the word STRAND}
   B = { x : x is a letter in the word STANDARD}
   C = { x : x is a letter in the word STANDING}
   Here A = B, B ≠ C, A ≠ C


7. Equivalent Set
   Two sets are equivalent if they have the same number of elements. It is not essential that the elements
   of the two sets should be same.
   As for example :
   A = {1, 2, 3, 4} B = { b, a, l, 1}.
   In A, there are 4 elements, 1, 2, 3, 4,
   In B, there are 4 elements, b, a, I,1 (one-to-one correspondence), Hence, A ≡ B (symbol ≡ is used to
   denote equivalent set)