## OPERATIONS ON SETS

(1) Union of Sets: The union of two sets A and B is the set of all the elements which are either in A or in B or in both A and B. It is denoted by . Let (2) Intersection of Sets: The intersection of two sets A and B is the set of […]

## LAWS OF SET OPERATIONS

(1) Idempotent laws : (2) Identity laws: (3) Commutative laws: (4) Associative laws: (5) Distributive Laws: (6) De-Morgan’s Laws:

## CARDINAL NUMBER OF SETS

Some important results derived from Venn diagrams are as follows: A, B and C are three sets. A and B are disjoint sets.

## VENN DIAGRAM

The pictorial representation of sets is called Venn diagram. The universal set is represented by a rectangular region and its subsets by circles inside the rectangle. In the above given Venn diagram, and and .   Here,and . If, there is no common elements in A and B and both are subsets of universal set, […]

## INTERVALS

(1) Closed Interval: Let a and b are two given real numbers such that , then (2) Open Interval: Let a and b are two given real numbers such that then or (3) Closed-open Interval: Let a and b are two given real numbers such that , then (4) Open-closed Interval: Let a and b […]

## SUBSETS

SUBSET: A set P is said to be a subset of a set Q if each element of P is also an element of Q. If P is subset of Q, we write PROPER SUBSET: If and then P is called a proper subset of Q and we write Example: Consider and Here, but Every […]

## EQUIVALENT AND EQUAL SETS

EQUIVALENT SETS Two finite sets A and B are equivalent only when number of elements of both the sets are equal. Example: A = {x : x is a natural number less than 6} B = {x : x is a vowel of English alphabet} n(A) = n(B) = 5 C = {2, 4, 6, […]

## FINITE AND INFINITE SETS

A set having definite number of elements is called finite set. In other words, we can say that the number of elements of a set is defined called finite set. A set which is not having definite number of elements is called infinite set. Example: A = {1, 2, 3, 4, 5, ……………., 100} B […]

## REPRESENTATION OF A SET

There are two types of representation: Tabular form Set – builder form  Tabular or roster form: A set is described by listing elements, separated by commas, in { } brackets. Example: The set of five prime numbers can be described as {2, 3, 5, 7, 11} The set of all months having 31 days described […]

## SETS : DEFINITION

The word ‘set’ in mathematics was first used by a German mathematician George Cantor (1845 – 1918). A set is a well-defined collection of objects. Well – defined means universal truth. The elements do not varies person to person. Set is denoted by capital letters of English alphabets. E.g. A, B, C, D, F, G, […]