Question

what is the difference between Relation and Function? explain with an example.​

Answer 1

Answer:

Relation- , the relation is defined as the collection of ordered pairs, which contains an object from one set to the other set. ... Functions- The relation that defines the set of inputs to the set of outputs is called the functions. In function, each input in the set X has exactly one output in the set Y.

Answer 2

Step-by-step explanation:

It is a kind of confusion in many students of India, including me. The main reason here is the incorrect way NCERT explains.

Many higher books have stated "Function" as a "Dependency" of one variable on other one. And that seems pretty much sensible if we continue our further studies in multidimensional calculus.

On the other hand the "SET- ELEMENT DEFINITION" for so called "Relation" can be adopted as a basic definition, but it also doesn't properly explain what a relation is.

Let me share my experience and make you feel the difference that I can't describe in words.

Say

R = {(x, y) : x and y are integers}

Here, it is a relation. There is a "Linguistic" Relation between x and y that they are integers, they may or may not be determinable by the given rule. There may be an infinite number of elements.

On the other hand let's say

R = {(x, y) : y = 2x and x is an integer}

Here, we have a CLEAR dependency of y on x. Hence, it is a function.

A function can be thought like a calculator or some kind of machine where you input any number, it processes the number with its own rule already programmed in it, and finally gives you the output (may be a single or multiple numbers). The set of all inputs is called Domain and that of all outputs is called Range.

What the problem actually research - oriented people may face with the SET - ELEMENT DEFINITION is that...

1. Let's say we have y = 2x. Here we have two sets containing all x's and all y's. A function is defined as a rule for choosing y for x from the corresponding sets. But when we step into higher dimensions say 4th or 5th, when we working with 4 or 5 variables at the same time, then it doesn't make sense anymore.

2. There are also some Parametric functions with which this definition don't fit.

So all the above things can be boiled up in these lines:-

"A relation from A to B is a set of all the elements in the sets A×B"

"A function is a special kind of relation where all the y's are unique for all x's."

- NCERT

Please note that "A function is a special kind of relation where all the y's are unique for all x's." is also not true.

Hope this all helps.