The supermodularity means for every $x'>x$ and $y'>y$, $$f(x',y') + f(x,y) > f(x',y) + f(x,y').$$

Suppose $f$ and $g$ are supermodular, non-negative and increasing in both arguments. Is the function $$ h(x,y) = \max\bigl( f(x,y) , g(x,y) \bigr) $$ supermodular?