Show Resource Allocation Problem is NP-Complete
Let's try to do some pattern matching. In independent set, we are given a graph, and want to find a maximum number of vertices satisfying some constraints. In your problem, we are given a collection of tasks and resources, and want to find the maximum number of resources satisfying some constraints. Hence it seems that tasks should correspond to vertices.

What about the constraints? In independent set, we are allowed to choose two vertices together if no edge connects them. In your problem, we are allowed to choose two tasks together if they have no common resource. Hence it seems that resources should correspond to edges.

You take it from here.