= Solution
For a <set function> $f:2^V\to\mathbb R$, the four properties are:
* A <normalised set function> satisfies \b[$f(\varnothing)=0$].
* A <nonnegative function> satisfies \b[$f(S)\geq0$ for every $S\subseteq V$].
* A <monotone set function> satisfies \b[$f(A)\leq f(B)$ whenever $A\subseteq B\subseteq V$].
* A <symmetric set function> satisfies \b[$f(S)=f(V\setminus S)$ for every $S\subseteq V$].
Here <monotone set function> means nondecreasing under inclusion; it does not require strict increase.
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