Question

Find R:A →A when A={1,2,3,4} such that
i) R= (a, b) / a-b = 10}
​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

$\sf{A = \{ \: 1,2,3,4 \} }$

$\sf{A \: Relation \: \: R : A \to \: A \: \: such \: that}$

$\sf{R = \{ \: (a, b) \: : \: a-b = 10} \: \}$

CALCULATION

It is given that

$\sf{A = \{ \: 1,2,3,4 \} }$

Now a relation from A to A is a subset of A × A

Where A × A is the Cartesian product of A and A

We we have to determine a Relation R with the below mentioned property

$\sf{A \: Relation \: \: R : A \to \: A \: \: such \: that}$

$\sf{R = \{ \: (a, b) \: : \: a-b = 10} \: \}$

Now there does not exist any ( a, b) in A × A such that a - b = 10

So the Required Relation is Empty

$\sf{Hence \: \: \: \: R = \Phi}$

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LEARN MORE FROM BRAINLY

Given set A = {1, 2, 3... 10)

Relation R is defined in set A as

R = {(a, b) € A × A: a = 2b}

Then range of relation R

https://brainly.in/question/23567484

Answer 2

Step-by-step explanation:

\displaystyle\huge\red{\underline{\underline{Solution}}}

Solution

TO DETERMINE

\sf{A = \{ \: 1,2,3,4 \} }A={1,2,3,4}

\sf{A \: Relation \: \: R : A \to \: A \: \: such \: that}ARelationR:A→Asuchthat

\sf{R = \{ \: (a, b) \: : \: a-b = 10} \: \}R={(a,b):a−b=10}

CALCULATION

It is given that

\sf{A = \{ \: 1,2,3,4 \} }A={1,2,3,4}

Now a relation from A to A is a subset of A × A

Where A × A is the Cartesian product of A and A

We we have to determine a Relation R with the below mentioned property

\sf{A \: Relation \: \: R : A \to \: A \: \: such \: that}ARelationR:A→Asuchthat

\sf{R = \{ \: (a, b) \: : \: a-b = 10} \: \}R={(a,b):a−b=10}

Now there does not exist any ( a, b) in A × A such that a - b = 10

So the Required Relation is Empty

\sf{Hence \: \: \: \: R = \Phi}HenceR=Φ

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

Given set A = {1, 2, 3... 10)

Relation R is defined in set A as

R = {(a, b) € A × A: a = 2b}

Then range of relation R

https://brainly.in/question/23567484