Suppose you have two time intervals, a and b. The following expression will tell you whether or not they
overlap:
a.start < b.end && b.start < a.end
Here's an interactive demo that illustrates how this works. The box labeled a is draggable. Each part of the
expression will appear green if it's true. If both parts of the expression are green, then the two time intervals
overlap.
a.start < b.end
&&
b.start < a.end
Allen's interval algebra
For a more exhaustive treatment of this topic, Allen's interval algebra provides a formalization of relations between time intervals.