Finding intersections, unions, and complements of sets is an essential issue in elementary mathematics. It builds the foundation for set theory, probability, logic, and other topics. It is commonly recognized that drawing a Venn diagram, which was first introduced by the British philosopher and mathematician John Venn in 1881, is a classic and effective way to represent items in abstract and discrete cases. However, Venn diagrams are not easy to use to find intersections, unions, and complements on intervals. To solve this problem, some teachers use the "shadow" that each set casts on the number line to represent intervals. This article introduces a more complete method developed in an effort to improve upon the use of the shadow method to find intersections, unions, and complements on intervals. The article also introduces an enhanced version--the "Undetermined Roof Method." These methods are not bound by the limitations of Venn diagrams and turn complicated problems into simple"roofs," making them easy to solve. More important, using the Roof Method allows the problem-solving procedure to resemble a game, which will intrigue high school students.