An open interval is the set of all numbers between a lower and upper bound. In mathematical notation, we write

(a, b) = { x | a < x < b }

Your task is to determine when two intervals overlap. For example, the intervals (1, 3) and (2, 4) overlap, as do (1, 4) and (2, 3). But the intervals (1, 2) and (3, 4) do not overlap.