  We consider the problem of jointly minimizing forms of two Boolean functions
$f, g \colon \{0,1\}^J \to \{0,1\}$ such that $f + g \leq 1$ and so as to
separate disjoint sets $A \cup B \subseteq \{0,1\}^J$ such that $f(A) = \{1\}$
and $g(B) = \{1\}$. We hypothesize that this problem is easier to solve or
approximate than the well-understood problem of minimizing the form of one
Boolean function $h: \{0,1\}^J \to \{0,1\}$ such that $h(A) = \{1\}$ and $h(B)
= \{0\}$. For a large class of forms, including binary decision trees and
ordered binary decision diagrams, we refute this hypothesis. For disjunctive
normal forms, we show that the problem is at least as hard as MIN-SET-COVER.
For all these forms, we establish that no $o(\ln (|A| + |B| -1))$-approximation
algorithm exists unless P$=$NP.
