Let A={(x, y): `x, y in z`, `x^(2)+y^(2) <= 16`}. Then the number of reflexive relations on set `A` 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.

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))

Prove that : =2|{:(1,1,1),(x,y,rz),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

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)