1. Find a SQL construct other than subquery, in, and not exists that if it appears in a SQL queries, the query may return false positive or negative over a database with null values. You may show the correctness of your answer using an example.

2. Find a SQL query that returns false negatives over databases with null values. Then, propose a transformation that translates this query to a SQL query that does not return any false positive and retains all true positives delivered by the original query over databases with null values. You may also find a SQL query that returns false positives over databases with null values and transform it to a query that does not return any false positive and retains all true positives delivered by the original query over a database with null values.

3. Find the largest subset of SQL queries that does not return any false positives over a database with null values.