Q4 Matemática  (Mediterranean Mathematics Olympiad 2006)

Seja $0\le x_{i,j}\le 1$, onde $i=1,2,\dots m$ e $j=1,2,\dots n$. Prove a desigualdade $$\prod _{j=1}^n\left(1-\prod _{i=1}^m{x}_{i,j}\right)+\prod _{i=1}^m\left(1-\prod _{j=1}^n(1-x_{i,j})\right)\ge 1$$