IntervalIntersection

IntervalIntersection[interval1, interval2, ...] gives the interval of points common to all intervals.

Examples

Find overlapping region:

IntervalIntersection[Interval[{0, 5}], Interval[{3, 10}]]
(* Interval[{3, 5}] *)

Non-overlapping intervals:

IntervalIntersection[Interval[{0, 2}], Interval[{5, 10}]]
(* Interval[] *)

Please visit the official Wolfram Language Reference for more details.