If `x` is a rational number and `y` is an irrational number, then both `x\ +\ y\ a n d\ x y` are necessarily rational both `x\ +\ y\ a n d\ x y` are necessarily irrational `x y` is necessarily irrational, but `x\ +\ y` can be either rational or irrational `x\ +\ y` is necessarily irrational, but `x y` can be either rational or irrational

Options

A. Both x + y and xy are necessarily irrational.
B. Both x + y and xy are necessarily rational.
C. xy is necessarily irrational, but x + y can be either rational or irrational.
D. x+y is necessarily irrational, but xy can be either rational or irrational.

Answer

D