In combinatorial mathematics, given a collection C of sets, a transversal is a set containing exactly one element from each member of the collection: it is a section of the quotient map inuced by the collection. If the original sets are not disjoint, there are several different definitions. One variation is that there is a bijection f from the transversal to C such that x is an element of f(x) for each x in the transversal. A less restrictive definition requires that the transversal just has a non-empty intersection with each member of C.