1. The problem statement, all variables and given/known data Same as title, where T maps from a set V to W, and U maps from W to Z. 2. Relevant equations 3. The attempt at a solution I know that the standard definition for a function being onto is that for all elements w in the codomain, there exists an element v in the domain such that T(v) = w. I am not sure exactly how to concretely apply this to show that U composed with T is also onto. To start, we have U(T(v)) = z, and we need to show that for all z in Z there exists a v in V such that that mapping is true. First we can use the fact that U is onto, which means there is always a w = T(v) that maps to z, and since T is onto, there is always a v that maps to w. Is this sufficient to show that UT is also onto? Is there a way to write this argument using less words?