Find a subset of R^2 which does not equal AXB for any subsets A and B of R. (R is real number) Solution The unit disk: the set of all points (x,y) such that x^2 + y^2 <= 1. A cartesian product of subsets of R is always a rectangle so any non-rectangular shape can not be stated as a cartesian product of subsets of R..

1. Find a subset of R^2 which does not equal AXB for any subsets A and B of R. (R is real number)
Solution
The unit disk: the set of all points (x,y) such that x^2 + y^2 <= 1. A cartesian product of subsets
of R is always a rectangle so any non-rectangular shape can not be stated as a cartesian product
of subsets of R.