SETS AND RELATION ( Part 2 )
TIPS AND FORMULAS
Set : Set is a collection of well defined objects which are distinct from each other. Sets are usually denoted by
capital letters A, B, C,...... and elements are usually denoted by small letters a, b, c,......
If a is an element of a set A, then we write a ∊ A and say a belongs to A or a is in A or a is a member
of A.
If a does
not belongs to A, we write a ∊ A.
Standard Notations :
N : A set of natural numbers.
W : A set of whole numbers.
z : A set of integers.
Z ๋ / Z¯ : A set of all positive/negative integers.
Q : A set of all rational numbers.
Q ๋ / Q¯ : A set of all positive/negative rational numbers.
R : A set of real numbers.
R ๋ / R¯ : A set of all positive/negative real numbers.
C : A set of all complex numbers.
Methods for Describing a Set :
(i) Roster/Listing Method/Tabular Form :
In this method, a set is described by listing element, separated by
commas, within braces.
e.g. A = {a, e, i, o, u}
(ii) Set Builder/Rule Method :
In this method, we write down a property or rule which gives us all the elements of
the set by that rule.
e.g. A = {x : x is a vowel of English alphabets}
Types of Sets
(i) Finite Set :
A set containing finite number of elements or no element.
(ii) Cardinal Number of a Finite Set :
The number of elements in a given finite set is called cardinal number of
finite set, denoted by n (A).
(iii) Infinite Set :
A set containing finite number of elements.
(iv) Empty/Null/Void Set :
A set containing no element, it is denoted by or {}.
(v) Singleton Set :
A set containing a single element.
(vi) Equal Sets :
Two sets A and B are said to be equal, if every element of A is a member of B and every element
of B is a member of A and we write A = B.
(vii) Equivalent Sets :
Two sets are said to be equivalent, if they have same number of elements.
If n(A) =n(B), then A and B are equivalent sets.
(viii) Subset and Superset :
Let A and B be two sets. If every element of A is an element of B, then A is called
subset of B and B is called superset of A.
Written as A B or B A
(ix) Finite Set :
If A is a subset of B and A B, then A is called proper subset of B and we write A B.
(x) Universal Set (U) :
A set consisting of all possible elements which occurs under consideration is called a
universal set.
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