If x y are real positive numbers show using the denition of

If x, y are real positive numbers, show (using the denition of positivity for reals) that xy is positive. (you can use without proof the fact that p > q > 0, r > s > 0 together imply pr > qs for p, q, r, s rational.)

Solution

Given x, y are positive real numbers then x>0 and y>0 then product xy>0 if xy<0 then either x or y should be negitive but this is not true since both x and y are positive