Functions and Relations

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Hello friends, in this blog we will understand the concept of Relations and Functions. Here we will discuss relation and function one by one. First we will talk about relation. Suppose we have given two sets I and J then relation 'R' can be defined from set 'I' to set 'J', is a subset of I * J. It is denoted in two forms that are given as:

List form

Tabular form

There are different types of relation which are shown below.

Ø Reflexive Relation

Ø Symmetric Relation

Ø Transitive Relation

Now we will see small introduction about all these given relations. First we will discuss reflexive relation.

Reflexive relation is a relation such that every element is related to itself. For example: (I, I) Є R for all i Є I.

Symmetric relation: Any relation 'R' is called as symmetric relation if (i, j) Є R = (k, i) Є R for all i, j Є I.

Transitive relation: Any relation 'r' is said to be a transitive relation if (i, j) Є R and (j, k) Є R => (i, k) Є R for all i, j, k Є I.

Now we will understand the concept of function.

Function is a group of ordered pair in which two terms present in pair must be different. Now we will discuss different types of function which are given as:

Ø One – one function

Ø Onto function

Ø Into function

Let’s have small introduction about all given functions. First we will understand the concept of one – one function.

One – one function - A function f: I → J is called as one – one function if every input term 'I' has different image in 'J'. So we can also write it as:

f : I → J is one – one if value of 'I' not equal to 'J'. (I ᚌ J) → f (I) ᚌf (J) for all IJ Ԑ I.

Molar Mass of Water is the mass of one mole of H₂O. Cbse sample paper for class x is helpful for preparation of board exams. In the next session we will discuss about Negative and Positive Numbers.