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