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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 toseparate 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 orapproximate than the well-understood problem of minimizing the form of oneBoolean 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 andordered binary decision diagrams, we refute this hypothesis. For disjunctivenormal forms, we show that the problem is at least as hard as MIN-SET-COVER.For all these forms, we establish that no $o(\ln (|A| + |B| -1))$-approximationalgorithm exists unless P$=$NP.

Inapproximability of a Pair of Forms Defining a Partial Boolean Function