GNU date and relatives dates

I was writing a simple script to delete some log files, all the log filenames contain the date of creation in the form YYYYMMDD and I needed to delete the files from previous month keeping the current month. The script will run on the last day of every month.

I thought the task will be very easy as I could use the GNU date command to build the date string, something like:

# The year
date +%Y

Use the date relative option for getting the previous month, something like:

date --date="-1 month" +%m

Then concatenate both strings and build a file pattern using wildcards like ? and *.

The system date was 2019-05-31 ahd I was expecting the 04 string as the output, instead 05 was printed.

I tried several variants and all printed the same, 05:

$ date --date="-1 month" +%m
05

$ date --date="last month" +%m
05

I DuckDuckGoed the Internet and found this answer:

https://stackoverflow.com/questions/13168463/using-date-command-to-get-previous-current-and-next-month

This is from the coreutils manual online:

https://www.gnu.org/software/coreutils/manual/html_node/Relative-items-in-date-strings.html#Relative-items-in-date-strings

$ date --date="$(date +%Y%m15) -1 month" +%m
04