Question 196
For a set $S$, let $|S|$ denote the number of elements in $S$. Let $A$ be a set of positive integers with $|A| = 2001$. Prove that there exists a set $B$ such that
(i) $B \subseteq A$;
(ii) $|B| \geq 668$;
(iii) for any $u, v \in B$ (not necessarily distinct), $u + v \notin B$.
(i) $B \subseteq A$;
(ii) $|B| \geq 668$;
(iii) for any $u, v \in B$ (not necessarily distinct), $u + v \notin B$.