&& and || in SQL are AND and OR.
Rewrite that to:
SELECT * FROM table WHERE (col1 = 4 AND col2 = 4) AND (col3 = 0 OR col4 = 0)
You can't use IN for column names. You can use IN like this:
WHERE col3 IN('4','a','another valid value')
,
which is equals to WHERE (col3 = '4' OR col3 = 'a' OR ...)
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