 Thus, the conditions on the right hand side emerge as properties of the sets \(\p(x,\abar)\). In fact, we can think of \(\forall\) and \(\exists\) as denoting these properties, i.e., the property of being identical to the universe, and of being non-empty, respectively. And now it is easy to think of other properties of sets that can also be treated as quantifiers, for example, the property of containing at least 5, or exactly 3, elements, or of being  infinite.[6]