If `R={(x,y):x,y in Z,x^(2)+3y^(2)<=8}` is a relation on the set of integers Z ,then the domain of `R^(-1) is

Let relation R defined on Z as follows R={(x,y),x in Z,y in Z,x^(2)=y^(2)), then find domain of R.

If R ={(x,y): x,y in Z , x^2 +y^2 =64} then , write R in the roaster form

If R={(x,y):x^(2)+y^(2)<=4;x,y in Z} is a relation on Z, write the domain of R.

Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3)):}|=|{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x)

If x , y, z in R, x + y + z= 4 and x^(2) + y^(2) + z^(2) = 6 , then the maximum possible value of z is

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))