Given a date in PostgreSQL

> select '2050-1-1'::date;
    date
------------
 2050-01-01

you can determine the day of the week for that date with the date_part() function

> select date_part('dow', '2050-1-1'::date);
 date_part
-----------
         6

The days of week are 0 through 6, 0 being Sunday and 6 being Saturday.

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