# Show Resource Allocation Problem is NP-Complete

We are given $$n$$ tasks and $$m$$ resources. Each task $$i$$ requires a set $$S_i$$ of resources to be active, and each resource can be used by at most one task. The Resource Allocation problem asks: given $$S_1, \ldots, S_n$$, and an integer $$k$$, whether it is possible to allocate the resources to the tasks so that at least $$k$$ tasks are active. Give a polynomial-time reduction from Independent Set to Resource Allocation

I am not sure how to construct the reduction. The difficulty I am having is the solver looks like a solver for a bipartite graph problem but we do not necessarily get a bipartite graph. Thank you!