A relation `R` is defined on the set `Z` of integers as: `(x ,y) in R x^2+y^2=25` . Express `Ra n dR^(-1)` as the sets of ordered pairs and hence find their respective domains.

Explanation

`R={(0,5),(0,−5),(3,4),(−3,4),(3,−4),(−3,−4),(4,3),(−4,3),(4,−3),(−4,3),(5,0),(−5,0)}`

`R^(−1)={(5,0),(−5,0),(4,3),(4,−3),(−4,3),(−4,−3),(3,4),(3,−4),(−3,4),(3,−4),(0,5),(0,−5)}`

Therefore domain of

R`={0,3,−3,−4,4,−5,−5}= `domain of `R^(−1)`