If R = (x, y) : x, y [ ] Z, x2 + 3y2 [ ] 8 is a relation on the set of integers Z, then th…

Question

If R = {(x, y) : x, y
$$ \in $$ Z, x2 + 3y2
$$ \le $$ 8} is a relation
on the set of integers Z, then the domain of R--1 is :

Accepted Answer

Given R = {(x, y) : x, y
$$ \in $$ Z, x2 + 3y2
$$ \le $$ 8}

So R =  {(0,1), (0,--1), (1,0), (--1,0), (1,1), (1,-1)

(-1,1), (-1,-1), (2,0), (-2,0), (-2,0), (2,1), (2,-1), (-2,1), (-2,-1)}

$$ \Rightarrow $$ R : { -2, -1, 0, 1, 2} $$ \to $$ {-1, 0, 1}

$$ \therefore $$ R-1 : {-1, 0, 1} $$ \to $$ { -2, -1, 0, 1, 2}

$$ \therefore $$ Domain of R--1 = {-1, 0, 1}

Solutions · 1