You can use date_trunc('week', ...).
For example:
SELECT date_trunc('week', '2012-07-25 22:24:22'::timestamp);
-> 2012-07-23 00:00:00
Then, you can convert this into a date, if you’re not interested in a start time.
To get the end date too:
SELECT date_trunc('week', '2012-07-25 22:24:22'::timestamp)::date
|| ' '
|| (date_trunc('week', '2012-07-25 22:24:22'::timestamp)+ '6 days'::interval)::date;
-> 2012-07-23 2012-07-29
(I’ve used the default formatting here, you can of course adapt this to use MM/DD/YYYY.)
Note that, if you want to make comparisons on timestamps, instead of using (date_trunc('week', ...) + '6 days'::interval, you might want to add an entire week and use a strict comparison for the end of the week.
This will exclude y timestamps on the last day of the week (since the cut-off time is midnight on the day).
date_trunc('week', x)::date <= y::timestamp
AND y::timestamp <= (date_trunc('week', x) + '6 days'::interval)::date
This will include them:
date_trunc('week', x)::date <= y::timestamp
AND y::timestamp < (date_trunc('week', x) + '1 week'::interval)
(That’s in the rare cases when you can’t use date_trunc on y directly.)
If your week starts on a Sunday, replacing date_trunc('week', x)::date with date_trunc('week', x + '1 day'::interval)::date - '1 day'::interval should work.