= Solution
{c}
Put $m=\lceil\log_2n\rceil$ and assign distinct complete <binary sequences> in $\{0,1\}^m$ to the $n$ points. For each coordinate $i$, let $A_i$ be the points with bit zero and $B_i$ those with bit one. Distinct sequences disagree in some coordinate, so these pairs form a <separating family of disjoint set pairs>.
Every point lies in exactly one side of every pair, hence the total incidence is $mn$, as allowed when $\lambda=1$. The construction reaches the bound:
$$
\boxed{m_{\min}=\lceil\log_2 n\rceil\quad(\lambda=1).}
$$
The reference to “(i)” in the original PDF's part (b) refers to part (a); the local TeX additionally duplicates that item.
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