[" 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 : "]

If R ={ (x,y) : x,y in z, x^(2) +y^(2) le 4 } is a relation on Z then domain of R 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^2le9} is a realation on Z, then domain of R is:

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)

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

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........