  In a 1908 paper Zermelo introduced a modified form of AC. Let us call a transversal (or choice set) for a family of sets \(\sH\) any subset  \(T \subseteq \bigcup \sH\)  for which each intersection \(T \cap X\) for \(X \in \sH\) has exactly one element.  As a very simple example, let  \(\sH = \{\{0\}, \{1\}, \{2, 3\}\}\). Then  \(\sH\) has the two transversals \(\{0, 1, 2\}\) and \(\{0, 1, 3\}\).  A more substantial example is afforded  by letting \(\sH\) be the collection of all lines in the Euclidean plane parallel to the \(x\)-axis. Then the set \(T\) of points on the \(y\)-axis is a transversal for \(\sH\).