Does a filtered index improve searching on the opposite condition?

Question

Does having a filtered index on a column improve queries with a WHERE clause that is the opposite of the filter condition?

Since the filtered index specifies what not to return, does it reduce the number of records to search?

Example:

CREATE TABLE MyTable
(
  ColumnA INT PRIMARY KEY CLUSTERED,
  ColumnB INT NULL
)

CREATE NONCLUSTERED INDEX IX_MyTable_Filtered_ColumnB
  ON MyTable (ColumnB)
  WHERE ColumnB IS NOT NULL

The index should improve this query:

SELECT ColumnA
FROM MyTable
WHERE ColumnB IS NOT NULL

Will it make any difference to this one?

SELECT ColumnA
FROM MyTable
WHERE ColumnB IS NULL

Answer 1

nope. You'll probably even get an error if you try to force your 'IS NULL' query to use your filtered index with an index hint.