Home
Class 11
MATHS
The relation R defined in A= {1, 2, 3} b...

The relation R defined in `A= {1, 2, 3}` by `aRb` if `|a^2-b^2| leq 5`. Which of the following is faise

A

R = {(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)}

B

`R^(-1)=R`

C

Domain of R = {1, 2, 3}

D

Range of R = {5}

Text Solution

Verified by Experts

Let a = 1
Then, `|a^(2)-b^(2)|le5implies|1-b^(2)|le5`
`implies|b^(2)-1|le5impliesb=1,2`
Let a = 2
Then, `|a^(2)-b^(2)|le5`
`implies |4-b^(2)|le5implies|b^(2)-4|le5`
`therefore b=1,2,3`
Let a = 3
Then, `|a^(2)-b^(2)|le5`
`implies |9-b^(2)|le5implies|b^(2)-9|le5impliesb=2,3`
`therefore R={(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3)}`
`R^(-1)={(y,x):(x,y)inR}`
`={(1,1),(2,1),(1,2),(2,2),(3,2),(2,3),(3,3)}=R`
Domain of R = `{x:(x,y)inR}={1,2,3}`
Range of `R={y:(x,y)inR}={1,2,3}`
Promotional Banner

Similar Questions

Explore conceptually related problems

The relation R defined in A= {1, 2, 3} by aRb if |a^2-b^2| leq 5 . Which of the following is false

The relation R defined in A= {1,2,3} by a R b if |a^(2)-b^(2)| le 5 . Which of the following is not true?

If the relation R is defined on the set A={1,2,3,4,5} by R={a,b} : |a^(2)-b^(2)| lt 8 . Then, find the relation R.

If the relation R be defined on the set A = {1,2,3,4,5} by R = {(a,b):|a^(2) -b^(2)| lt 8} . Then , R is given by .............

The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b): |a^(2)-b^(2)|lt16} is given by

The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b): |a^(2)-b^(2)|lt16} is given by

If the relation R be defined on the set A={1,2,3,4,5} by R={(a,b): |a^(2)-b^(2)|lt 8}. Then, R is given by …….. .

If the relation R be defined on the set A={1,2,3,4,5} by R={(a,b): |a^(2)-b^(2)|lt 8}. Then, R is given by …….. .