What is a "positive statement" in mathematical proof?
In this situation, it seems that a negative statement is a proposition that comes with a logic negation in front of it. Let me try to explain it with an example, that should be clearer:
Positive statement: “There exists a function $f:X \rightarrow Y$ such that $f(x)$ is constant on $X$“
Negative statement: “There does not exist a function $f:X \rightarrow Y$ such that $f(x)$ is constant on $X$“, that logically means “for every function $f:X \rightarrow Y$, $f(x)$ is not constant on $X$ (that is there exists at least an $a$ and $b$ both in $X$ such that $f(a) \neq f(b)$.