IntervalMemberQ
IntervalMemberQ[interval, x] gives True if x lies within the interval, and False otherwise.
IntervalMemberQ[interval1, interval2] gives True if interval2 is completely contained in interval1.
Examples
Check membership:
IntervalMemberQ[Interval[{0, 10}], 5]
(* True *)IntervalMemberQ[Interval[{0, 10}], 15]
(* False *)Please visit the official Wolfram Language Reference for more details.