154780

x+y<1+xy

For any given number for x and y between 0 and 1, take 1-x and 1-y.
(1-x)(1-y) > 0
When expanded leaves 1+xy-x-y > 0
Adding x and y to both sides gives 1+xy > x+y
Therefore, due to the fact that x and y both lie between 0 and 1, this inequality is equal to x+y<1+xy.