# Functions and Relations

**Functions and Relations**

**Introduction:**

Relation

**A Relation is a set of ordered Pairs that satisfy a relationship.**

**For Example:**

**PXQ**

**PXQ = {(2,10), (2,20), (2,35), (4,10), (4,20), (4,35)}**

**PXQ = {(p, q): p ɛ P, q ɛ Q}**

**Relation ‘R’ → ALL (p, q) that satisfies ‘R’**

**R’ = {(p, q): q is a multiple of p, p ɛ P, q ɛ Q}**

**R’ = {(2, 10), (2, 20), (4, 20)}**

This entire circle represents the set of elements in the Cartesian PXQ.

In that case set R’ will be a part of it. We can say that set R’ is a subset of Cartesian product PXQ. That is the basic concept of relation.

A Relation is a set of order pairs that satisfy a Relationship.

**We come across various functions. But very few understand what a function is. It’s simply a function is like this box with two pipes.**

**It gets an input. Some operation takes place inside and it gives an output based on the operation that occurred inside all that matters is what occurs inside.**

**Let’s understand an example.**

**Let this be a function box.**

**The operation it does inside is that it multiplies every input with 5 and gives**

**an output. This box gets 2 as an input. It will multiply 2 with 5 and give**

**an output of 10.**

**Similarly if it gets 3 as an input it will give 3 times 5 and 15 as**

**the output. If 4 is the input it will give us 20 as the output.**

**So this box is our function the function is written as F(X ) equals 5(X)**

**Make sure you understand this well it means that if we**

**substitute X with any number this function will give us an output 5 times**

**that number. So F(2 )will be 5(2) which is 10**

**Function and Relation Examples**

**Example : Find A X B, A X B and B X A**

**1) A={2,-2,3} and B={1,-4}**

**A X B={(2,1), (2,-4), (-2,1), (-2,-4), (3,1) (3,-4)}**

**A X A={(2,2), (2,-2), (2,3), (-2,2), (-2,-2), (-2,3), (3,2), (3,-2), (3,3)}**

**B X A {(1,2), (1,-2), (1,3), (-4,2), (-4,-2), (-4,3)}**

**A X B={(p , p), (p , q), (q , p), (q , q)}**

**A X A={(p , p), (p , q), (q , p), (q , q)}**

**B X A={(p , p), (p , q), (q , p), (q , q)}**

**A X A={} = {(m , m), (m , n), (n , m), (n , n)}**

for more example click here

So, These are some of the examples for Functions and Relations. Which are explained in the top of the section. Two numbers go to gather is known as order pair of number. Where a Relation is a set of ordered Pairs that satisfy a relationship.

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