Sets and Relations

Introduction about Sets and Relations:

           A group of elements is called a set when the elements in the group are distinct. A characteristic of two objects is called Relation.

Example for Set:

            The collection of all natural numbers
            The collection of all equilateral triangles in a plane.
   Let us learn more about sets and relations in this chapter.

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More about Sets:

           An object of a set is called an element or a member or an individual of the set. We usually denote a set by an upper-case letter like A or B and an element of a set by a lower-case letter such as x or y. If x is an element of a set A, we indicate this fact symbolically by writing    x ? A. The symbol ? stands for ‘is an element of’ or ‘is a member of ’or ‘belongs to’. When an object x is not an element of the set A, we denote this fact by writing x ? A. Here, the symbol ? stands for ‘is not an element of’ or ‘is not a member of’ or ‘does not belong to’.

             For example, if A is the set {1, 3, 4, 5}, then the elements of A are 1, 3, 4 and 5; that is, we have 1 ? A, 3 ? A, 4 ? A and 5 ? A. We note that 6 ? A, -11 ? A, 9 ? A,

Types of Relations:

A relation is said to be a reflexive for the each element ‘a’ ? A. (a R a) Here R represents the relation.
A relation is said to be a reflexive for the each element ‘a’?  A. The element a is not related to a.
A relation is said to be a symmetric for the element a ~ b then b ~ a.
A relation is said to be a anti symmetric for the element a~ b then b  a.
A relation is said to be a transitive for the element aRb and bRc then aRc