Representation of sets (how to represent a set)

DISCRETE MATHEMATICS - 2 

UNIT -1 : SETS , RELETAIONS AND FUNCTIONS

 

How to represent a set ?

SET REPESNETATION:-

                               

        There are three ways to represent a set, they are -

List representation.

Predicate representation

 Missing element representation 

 1. List representation: -

                 Let us suppose we have a set 'A' with elements 1, 2, 3, a and b generally a set is represented by listing all the elements of it. Here set A is represented by

                                     A = {1, 2, 3, a, b} 

               Here elements are simply listed within the pair of brackets ({}).

2.Predicate representation of  a set : -

                        

               In this representation, a set is defined by a predicate , this representation is more convenient then list representation.

    For examples: -

                     

                       B = {x | x is an odd positive integer}

                       

                       | indicate such that.

           

              Let us suppose that p(x) denote "x is an odd positive integer" then 

                        

                      B = {x | p(x)}

         If we want to tell that some element b belongs to a set B then for this p(b) has to be true.

    

               For examples: - 

                                     1 ∈ B because 1 is an odd positive integer. 2 ∉ B because 2 is not an odd positive integer number so 2 does not belongs to the set B .

             

               The set which are usually specified by predicates.

 

               For examples: -  A = { 1, 2, 3, a, b} is not equivalent to the set 

                              

                              A = {x | (x=1) v (x=2) v (x=3) v (x=a) v (x=b)}      

3. Missing element representation  : -  

                      

                     Sometimes it is convenient to represents sets by missing element representation . 

 Examples: -   

                  B =  {x | x is an odd positive integer }

                  B =  {1, 3, 5, ...}

 also  see sets