Let `X={1,2,3,4,5,6,7,8,9}.` Let R be a relation in `X` given by `R_1={(x,y):x-y` is divisible by `3}` and `R_2` another on `X` given by `R={(x,y):(x,y)uu{1,4,7}} or {x,y} uu {2,5,8} or {x,y} uu {3,6,9}}` Show that `R_1=R_2.`

Explanation

Here, `X = {1,2,3,4,5,6,7,8,9}`

`R_1 = {(x,y): x-y` is divisible by `3}`

As, `x-y` is divisible by `3`.

`x-y = 3n` where `n in N`

`=>x= y+3n`

`y=1, x = 4` when `n=1`

`y=1, x = 7` when `n=2`

`y=4, x = 7` when `n=1`

...