Question

3. Domain of {(x,y)/x-y=6, x,yEn}​

Answer 1

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

FORMULA TO BE IMPLEMENTED

Let A and B are two non empty sets

Let R be a relation from A to B

Then the domain of the relation is the set of those values of x for which the relation holds.

In othe words

$\sf{Domain \: of \: R \: = \{ \: x : (x, y) \in \: R \: } \}$

TO DETERMINE

$\sf{Domain \: of \: \{(x,y) : x-y=6, (x,y) \in \: \mathbb{N} \: \}}$

CALCULATION

Let R be the given relation

Then

$\sf{ \: R = \{(x,y) : x-y=6, (x,y) \in \: \mathbb{N} \: \}}$

From above

$\sf{ x - y = 6\: }$

$\implies \: y = x - 6$

$\sf{ \: For \: x = 7 \: \: we \: get \: y = 7 - 6 = 1 }$

$\sf{ \: For \: x = 8 \: \: we \: get \: y = 8 - 6 = 2 }$

$\sf{ \: For \: x = 9 \: \: we \: get \: y = 9 - 6 =3}$

$\sf{ \: For \: x = 10 \: \: we \: get \: y = 10 - 6 = 4 }$

.

.

.

So the given relation can be rewritten as

$\sf{R = \{( 7, 1) , ( 8,2), (9,3), (10, 4),........ \} }$

Hence

$\sf{Domain \: of \: R \: = \{ 7,8,9,10,.......... \}}$

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

Let A = (1,8,27,64,125) and B= (1,2,3,4,5,6)

and R be the relation ‘is cube of 'from A to B

then domain of R is

https://brainly.in/question/21096862