# Choosing which workers (limited number) to use in a binary assignment problem?

First of all, I am not completely sure whether this problem belong to the category of assignment problems so feel free to correct me in this case.

The problem:

We are given a set of $$m$$ workers $$A = \{ a_1, a_2,...a_m \}$$ and a set of $$n$$ tasks $$T = \{ t_1, t_2,...,t_n \}$$. Each worker either can or cannot perform any given task and there is no cost associated with a task. The set of tasks that can be performed by a single worker $$a_i$$ is $$T_{a_i} \subset T$$. The set of tasks that can be performed by a subset of $$s$$ workers is given by the union of the tasks each individual worker can perform $$\bigcup_{i=1}^{s} T_{a_i}$$ (not necessarily the first $$s$$ workers).

The problem is to select $$s$$ workers such that the number of task that can be performed is maximized, i.e. maximize the number of elements in $$\bigcup_{i=1}^{s} T_{a_i}$$.

I couldn't find which category of problems this belong to, let alone any solutions. Any help in this matter would be greatly appreciated!