Sets Definition and Notations

Set:           

        What is a set? A set is a well-defined collection of distinct objects. Each object in a set is known as a member an element of the set. The elements may be ANYTHING!. The sets are denoted by capital letters A, B, C etc and  the elements of sets are denoted by small letters for e.g x, y ,z . For example if I talk about the Set A of all positive even numbers below 10, my set would consist the elements : A= {2,4,6,8}

                   

         

Equal Sets:

                   Two sets A and B are equal if they have exactly the same elements in them are called and written as A=B

 equal sets .

Finite set:

                A set having limited number of elements is called finite set. For example

                                 A={2,4,6,8,10}

Infinite set:

                A set having unlimited number of elements is called in finite set. For example

                                A={2,4,6,8,10…………………}

Null or Empty Set:

                               A set having no element is called a null set or an empty set. It is denoted by { } or ∅.

Subset:

            If every element in Set A is also in Set B, then Set A is called a subset of Set B and denoted by  A⊆ B
Absolute or Epsilon or Universal set     :              

                                                       It is denoted by 'є' or ‘U’. A set that contains all those sets which are given. For example  if I talk about Sets A and B. Then these sets will actually be the subsets of the universal set. Universal set holds great importance for it can be used to impose restrictions so that the elements in the sub-set can be kept within limits. For e.g if I say the universal set has numbers 1 to 10 only. Then I add that Set A (part of that universal set) is made up of odd numbers. Its elements would be : 1,3,5,7,9 . It would stop at 9 even though 11,13 onwards are also odd numbers. Why? Because you have to stay within the limits of the universal!

 Operations on sets:

                                Suppose we have four sets - A, B, C, and D. Let these sets be defined as follows:  

                              A = {2,3}; B = {1, 2}; C= {2, 3, 4}; and D = {1, 2, 3, 4}.

 Union of Two Sets:

                     The union of two sets A and B  is the set that has all the elements present in A or B or both of the two sets.  It is denoted by A ∪ B. For example

                                                   A U B = {1,2,3}

 Intersection of Two Sets:

                                    The intersection of two sets A and B  is the set that has all the elements present in A and B both.  It is denoted by A ∩ B. For example

                                                    C ∩ D= {2,3,4}

Intersection of sets

By: Baqar Ali