Question

identify distinction between a relation and a function with suitable examples and illustrate graphically​

Answer 1

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TO IDENTIFY

The distinction between a relation and a function with suitable examples and to illustrate graphically

EVALUATION

RELATION

Let S and T be two non empty sets. A relation R between S and T is a subset of S × T

EXAMPLE

Let S = { 2 , 3 , 4 , 5 } and

T = { 11 , 12 , 13 , 14 }

A relation R between S and T defined as

$\sf{ R = \{(a, b) : a \: is \: a \: divisor \: of \: b \: \} }$

$\sf{Then \: \: R = \{ (2,12),(2,14),(3,12),(4,12) \}}$

Here 2 in S is related to two elements 12 & 14 of T , but 5 in S in not related to no element of T by the relation R

FUNCTION

Let A and B are two non empty sets. If f is a relation between A and B with the property that every element x of A is related exactly one element y of B is said to be a Function from A to B

EXAMPLE

Let S = { 2 , 3 , 4 , 5 } and

T = { 11 , 12 , 13 , 14 }

$\sf{Now \: \: f = \{(2,11),(3,12),(4,13),(5,13) \}}$

Then every element x of A is related exactly one element y of B

Hence f is a function

GRAPHICAL ILLUSTRATION

A Venn Diagram related to above Relation and function is attached in the attachment

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