Set:- A set is a well defined collection of distnict objects.
Here it is important to understand the meaning of term ‘well defined’. Let us take an example to understand it . Suppose there are 30 students in class eleventh, I asks you to make list boys then you can easily do it, if same task is given to two more students then they will also easily do it and the list of all of you will contain same students. Why? The answer is simple because the term “make list of boys” is well defined. Now if I ask to write name of three students having good learning abilities then no two answers could be same. Why? Because the term “good learning abilities” is not well defined everyone will make decision according to his own understanding and ability .
You Can find some more terms which are well defined or not well defined
e.g. students having marks more than 80% in class 10th (is well defined )
students good in mathematics ( not well defined)
Therefore a set is simply a list of objects which are called elements or members of sets.
Sets are generally denoted by capital letters. i.e. A,B,C, etc.
Its elements are represented by small letters a,b,c, etc.
If ‘a’ is an element of set A then we write it or aϵA (a belongs to A)
If ‘a’ is not an element of set A then we write it as a∉A (a does not belong to A)
Some more sets and their symbols
N : set of natural numbers
Z : set of all integers etc.
Representation of sets: There are two methods to represent a set
- Roster form or Tabular form
- Set Builder form
In roster form all the element of a set are listed without repetition as
A ={a,e ,i,o,u }
In set builder form a single common property possessed only by of all the elements of the set is written as
A = {x:x is a vowel in the English alphabet}