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The definition of Supermodularity is that for every $x′>x$ and $y′>y$, \begin{equation*} f(x′,y′)+f(x,y)>f(x′,y)+f(x,y′). \end{equation*} Suppose $f$ and $g$ are supermodular, non-negative and increasing in both arguments. Is the function $h(x,y)=f(x,y)*g(x,y)$ supermodular?

The definition of Supermodularity is that for every $x′>x$ and $y′>y$, we have \begin{equation*} f(x′,y′)+f(x,y)>f(x′,y)+f(x,y′). \end{equation*} Suppose $f$ and $g$ are supermodular, non-negative and increasing in both arguments. Is the function $h(x,y)=f(x,y)*g(x,y)$ supermodular?

The definition of Supermodularity is that 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 $h(x,y)=f(x,y)*g(x,y)$ supermodular?

The definition of Supermodularity is that for every $x′>x$ and $y′>y$, \begin{equation*} f(x′,y′)+f(x,y)>f(x′,y)+f(x,y′). \end{equation*} Suppose $f$ and $g$ are supermodular, non-negative and increasing in both arguments. Is the function $h(x,y)=f(x,y)*g(x,y)$ supermodular?