Question

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}

Answer 1

Correct Answer - D
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}`