I will calculate last Sunday and last Saturday on every Monday.
E.g. today is 08 July 2013 Monday
last Sunday: 30 June 2013 00:00:00
last Saturday: 6 July 2013 23:59:59.
Note the last Sunday is from 00:00:00 and last Saturday is until 23:59:59
Given your question, where the query will be run only on Mondays and the objective is to obtain the dates as stated above, one way to solve it is:
SELECT TRUNC(SYSDATE) AS TODAYS_DATE, TRUNC(SYSDATE)-8 AS PREVIOUS_SUNDAY, TRUNC(SYSDATE) - (INTERVAL '1' DAY + INTERVAL '1' SECOND) AS PREVIOUS_SATURDAY FROM DUAL
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