To check time if it avialble in mysql

time_range_in_sql

Assuming Date Range 1 :: User Input
Date Range 2 :: Database Row

Intersection
Date Range 1   |         |>----------------------<|
Date Range 2   |                 |>------------------------<|
where Range1Start <= Range2End and Range1End >= Range2Start

Range 1 in Range 2:
Date Range 1   |                   |>-------------<|
Date Range 2   |                 |>------------------------<|
where Range1Start >= Range2Start and Range1End <= Range2End

Range 2 in Range 1:
Date Range 1   |         |>----------------------<|
Date Range 2   |                 |>-------------<|
where Range2Start >= Range1Start and Range2End <= Range1End

14:00:00 -> 18:00:00 (Stored In DB)

1) 15:00:00 -> 19:00:00 :: True (intersection date to the left)
2) 12:00:00 -> 17:00:00 :: True (intersection date to the right)
3) 10:00:00 -> 13:00:00 :: False (before date range 2)
4) 19:00:00 -> 21:00:00 :: False (after date range 2)
5) 15:00:00 -> 16:00:00 :: True (Subset)
6) 13:00:00 -> 19:00:00 :: True (Superset)

Sample Sql in #2 ::
SELECT * FROM Room WHERE
('12:00:00' <= `end_time` AND '17:00:00' >= `start_time`) OR
('12:00:00' >= `start_time` AND '17:00:00' <= `end_time`) OR
(`start_time` >= '12:00:00' AND `end_time` <= '17:00:00')