Let `A\ ` be the set of first five natural numbers and let `R` be a relation on A defined as follows `(x , y) in RhArrxlt=ydot`. Express `R\ a n d\ R^(-1)` as sets of ordered pairs. Determine also The domain of `R^(-1)` The range of `Rdot`

Explanation

Given

`A\ `
is the set of first five natural numbers and
`R`
be a relation on A defined as follows `(x , y) in RhArrxlt=ydot`

So,`R={(1,1),(1,2),(1,3),(1,4),(1,5),(2,2),(2,3),(2,4),(2,5),(3,3),(3,4),(3,5),(4,4),(4,5),(5,5)}`

`R^(−1)={(1,1),(2,1),(3,1),(4,1),(5,1),(2,2),(3,2),(4,2),(5,2),(3,3),(4,3),(5,3),(4,4),(5,4),(5,5)}`

domain`(R^(−1))={1,2,3,4,5}= `range `(R)`