Postgres: first and last days of any month - postgresql

Question

I have two date columns in postgres: 'StartDate' and 'EndDate'.
I need to assign various combinations of date ranges with a different code.
e.g
IF StartDate = EndDate THEN 'a'
What I'd like to be able to do is select any row in which the StartDate is the first day of any month AND the EndDate is the last day of any month. (IF StartDate = FirstDayOfMonth AND EndDate = LastDayOfMonth THEN 'b').
e.g. when StartDate = '01-02-2011' and EndDate = '31-05'2012' then'b', or StartDate = '01-11-1996' and EndDate = '31-01-2001' then 'b'.

Answer 1

The easiest to get the first and last day of a month is to rely on date arithmetics, e.g.:
# select date_trunc('month', now()::date);
date_trunc
------------------------
2014-12-01 00:00:00+01
(1 row)
# select date_trunc('month', now()::date)
+ interval '1 month'
- interval '1 day';
?column?
------------------------
2014-12-31 00:00:00+01
(1 row)
If needed, note that you can use generate_series() to compute the full list between two dates:
select d as first_day,
d + interval '1 month' - interval '1 day' as last_day
from generate_series('2014-01-01'::date,
'2014-12-01'::date,
'1 month') as d;
first_day | last_day
------------------------+------------------------
2014-01-01 00:00:00+01 | 2014-01-31 00:00:00+01
2014-02-01 00:00:00+01 | 2014-02-28 00:00:00+01
2014-03-01 00:00:00+01 | 2014-03-31 00:00:00+02
2014-04-01 00:00:00+02 | 2014-04-30 00:00:00+02
2014-05-01 00:00:00+02 | 2014-05-31 00:00:00+02
2014-06-01 00:00:00+02 | 2014-06-30 00:00:00+02
2014-07-01 00:00:00+02 | 2014-07-31 00:00:00+02
2014-08-01 00:00:00+02 | 2014-08-31 00:00:00+02
2014-09-01 00:00:00+02 | 2014-09-30 00:00:00+02
2014-10-01 00:00:00+02 | 2014-10-31 00:00:00+01
2014-11-01 00:00:00+01 | 2014-11-30 00:00:00+01
2014-12-01 00:00:00+01 | 2014-12-31 00:00:00+01
(12 rows)

Answer 2

You can extract the day part of the date and check its value. For the first day of the month it should be 1, and for the last - you simply add one day to the date and check whether it is the first day of the next month, this would mean that the original date is the last day of the current month.
...
CASE WHEN
EXTRACT('day' FROM StartDate) = 1
AND
EXTRACT('day' FROM EndDate + '1 day'::interval) = 1
THEN 'b'
...