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Let X={1,2,3,4,5,6,7,8,9}. Let R be a re...

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.`

Text Solution

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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`
...
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