Question 25
Find all functions $f : \mathbb{R} \to A$ such that
i. $x \in f(y)$ if and only if $y \in f(x)$.
ii. $|x - y| \gt 2$ if and only if $f(x) \cap f(y) = \emptyset$.
iii. For all real numbers $0 \le r \le 1$; $f(r) = [r^2 - 1, r^2 + 1]$.
i. $x \in f(y)$ if and only if $y \in f(x)$.
ii. $|x - y| \gt 2$ if and only if $f(x) \cap f(y) = \emptyset$.
iii. For all real numbers $0 \le r \le 1$; $f(r) = [r^2 - 1, r^2 + 1]$.