Introduction to Set Theory

  1. A set is a well-defined collection of objects.

˜   2. There are two methods of representing a set :–

               (a)  Roster or Tabular form.

               (b) Set-builder form or Rule method.

  3.Types of sets

(i)        Empty set or Null set or void set

(ii)      Finite set

(iii)     Infinite set

(iv)     Singleton set

 4.˜  Subset: – a set A is said to be a subset of set B if an element a Î A Þ a Î B, for " a Î A.

 5. Equal sets: – Two sets A and B are equal if they have exactly the same elements i.e.              

                               A = B if A Ì B and B Ì A

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  6. Power set : The collection of all subsets of a set A is called power set of

A, denoted by P (A) i.e. P (A) = {B: B Ì A}

˜  7. If A is a set with n (A) = m then n [P (A)] = 2^m

˜  8. Types of Intervals: -

(i)    Open Interval (a, b) = {x Î R : a < x < b}

(ii)  Closed Interval [a, b] = {x Î R : a ≤ x ≤ b}

(iii) Semi open or Semi closed Interval,

    (a, b] = {x Î R: a < x ≤ b}

    [a, b) = {x Î R: a ≤ x < b}

       9. Union of two sets A and B is:

       10. Intersection of two sets A and B is:

       11. Disjoint sets: Two sets A and B are said to be disjoint if A Ç B = Ф

   

        12. ˜Difference of sets A and B is,

       13. ˜Difference of sets B and A is,

       14. ˜˜  Complement of a set A, denoted by A' is

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