Let $G(m,n)$ be A bipartite graph $G$ with paritions $m$ and $n$ with the property that partition $\mathit n$ has two types of nodes (type1 or type2).
Given $G(m,n)$ and $k \in \mathbb Z+$:
Does $\mathit S\subset \mathit m$ where |$\mathit S$| $=$ $\mathit k$ exist so that none of $\mathit S$'s nodes are adjacent to nodes of type1, but all type2 nodes in $n$ are adjacent to nodes in $S$? ($S$ is a subset of the $m$ partition).
I can see a solution is easily verified by checking that each type2 in $n$ has a neighbor in $S$ and that |$S$| $=$ $k$. This means the problem is in NP.
To reduce the problem of Set Packing to the above, I am thinking to consider the of all of $m$ nodes's neighborhoods as subsets. But from here I am not sure how to proceed with the problem mapping.