Math, asked by namku, 1 year ago

i need an explanation of how ror^-1 was derived from the above 2 sets

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Answered by rational

$R=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}$

Get $R^{-1}$ by swapping coordinates :
$R^{-1}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}$

the composition $R\,\circ\,R^{-1}$ can be obtained by seeing the possible points of R for each value of $R^{-1}$ :
$R^{-1}(3)=1,2\implies\,R\,\circ\,R^{-1}(3)=R(1),R(2)=3,5$

that means, the composition $R\,\circ\,R^{-1}$ maps $3$ to $3$ or $5$ . therefore you get points $(3,3)$ and $(3,5)$

rational: what are the values of R^(-1)(5) ?

rational: simply look at R^(-1) row, 5 is getting mapped to 1,2 yes ?

rational: that means R^(-1)(5) = 1 or 2

namku: u said to see posiible points of r for each value of r inverse but r inverse of 5 doesnt have any points in r

rational: we need to see where 1, 2 are getting mapped to in R

rational: 5 ------>R^(-1)------->1 or 2-------R-------> 3 or 5

rational: therefore RoR^(-1)(5) = 3 or 5

rational: and you get points (5, 3) and (5, 5)

namku: got it thanks a lot

rational: np:)

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