If R be a relation from A-1-2-3-4 to B-1-3-5 i-e- -a-b- -R-a b-then-RoR-1 is -1- 3- -1- 5- -2- 3- -2- 5- -3- 5- -4- 5-3- 1- -5- 1- -3- 2- -5- 2- -5- 3- -5- 4-3- 3- -3- 5- -5- 3- -5- 5-3- 3- -3- 4- -4- 5-

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Inverse of a Function

If R be a rel...

Question

If R be a relation $<$ from A={1,2,3,4} to B={1,3,5} i.e., (a,b) $\in R \Leftrightarrow a < b, t h e n R o R^{- 1}$ is

{(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

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{(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

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{(3, 3), (3, 5), (5, 3), (5, 5)}

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{(3, 3) (3, 4), (4, 5)}

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Solution

The correct option is C
{(3, 3), (3, 5), (5, 3), (5, 5)}

We have, $R$ ={(1,3);(1,5);(2,3);(2,5);(3,5);(4,5)}
$R^{- 1}$ = {(3,1);(5,1);(3,2);(5,2);(5,3);(5,4)}
Hence $R o R^{- 1}$ = {(3,3);(3,5);(5,3);(5,5)}

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If R be a relation < from A={1,2,3,4} to B={1,3,5} i.e., (a,b) ∈ R ⇔ a<b, then RoR−1 is

The correct option is C {(3, 3), (3, 5), (5, 3), (5, 5)} We have, R={(1,3);(1,5);(2,3);(2,5);(3,5);(4,5)} R−1 = {(3,1);(5,1);(3,2);(5,2);(5,3);(5,4)} Hence RoR−1 = {(3,3);(3,5);(5,3);(5,5)}

If R be a relation $<$ from A={1,2,3,4} to B={1,3,5} i.e., (a,b) $\in R \Leftrightarrow a < b, t h e n R o R^{- 1}$ is

The correct option is C
{(3, 3), (3, 5), (5, 3), (5, 5)}

We have, $R$ ={(1,3);(1,5);(2,3);(2,5);(3,5);(4,5)}
$R^{- 1}$ = {(3,1);(5,1);(3,2);(5,2);(5,3);(5,4)}
Hence $R o R^{- 1}$ = {(3,3);(3,5);(5,3);(5,5)}