SQL Server 2012 and NULL comparison - sql-server

Question

Can anyone explain me why these two statements returns different results?
SELECT CASE WHEN NOT((NULL = NULL) OR (1 != 1)) THEN 1 ELSE 0 END
SELECT CASE WHEN NOT((NULL = NULL) AND (1 != 1)) THEN 1 ELSE 0 END
I know that NULL compared with anything gives false and I wanted to use that property but I stopped at commands similar to above. My real statements instead of NULLs use variables that can be NULL but I simplified them to show where is the problem. I thought that it has something with operation order but it seems that's not it.

Answer 1

I know that NULL compared with anything gives false
This isn't correct, NULL compared with anything evaluates to unknown, not false, a quick example:
SELECT CASE WHEN (NULL = NULL) THEN 'True'
WHEN NOT(NULL = NULL) THEN 'False'
ELSE 'Other'
END
Will give the third option of Other.
If we rewrite your logic (still the same meaning, but it becomes more clear):
SELECT CASE WHEN (NULL <> NULL) AND (1 = 1) THEN 1 ELSE 0 END
SELECT CASE WHEN (NULL <> NULL) OR (1 = 1) THEN 1 ELSE 0 END
So in the first instance you have WHEN [Unknown] AND [True] which is false, but in the second you have WHEN [Unknown] OR [True] which is true, so returns 1.
If you rewrite the query with variables, then inspect the execution plan XML, you can see that SQL Server rewrites the expression as above during compilation:
DECLARE #a INT = NULL, #b INT = NULL, #c INT = 1, #d INT = 1;
SELECT TOP 1
CASE WHEN NOT((#a = #b) OR (#c != #d)) THEN 1 ELSE 0 END,
CASE WHEN NOT((#a = #b) AND (#c != #d)) THEN 1 ELSE 0 END

Answer 2

-- first query
SELECT CASE WHEN NOT((NULL = NULL) AND (1 != 1)) THEN 1 ELSE 0 END
=
SELECT CASE WHEN NOT(unknown AND false) THEN 1 ELSE 0 END
=
SELECT CASE WHEN NOT(false) THEN 1 ELSE 0 END
=
SELECT CASE WHEN true THEN 1 ELSE 0 END
=
1
-- second query
SELECT CASE WHEN NOT((NULL = NULL) OR (1 != 1)) THEN 1 ELSE 0 END
=
SELECT CASE WHEN NOT(unknown OR false) THEN 1 ELSE 0 END
=
SELECT CASE WHEN NOT(unknown) THEN 1 ELSE 0 END
=
SELECT CASE WHEN unknown THEN 1 ELSE 0 END
=
else matched, so 0
And to D0dger's question from comments:
It's more interesting why SELECT CASE WHEN (NULL = NULL) OR (1 != 1) THEN 1 ELSE 0 END and SELECT CASE WHEN NOT((NULL = NULL) OR (1 != 1)) THEN 1 ELSE 0 END returns 0
SELECT CASE WHEN (NULL = NULL) OR (1 != 1) THEN 1 ELSE 0 END
=
SELECT CASE WHEN unknown OR false THEN 1 ELSE 0 END
=
SELECT CASE WHEN unknown THEN 1 ELSE 0 END
=
else matched, so 0
OR (Transact-SQL), AND (Transact-SQL)

Answer 3

So, there are 2 options: Either you have ANSI_NULLS ON (and you should) or you have ANSI_NULLS OFF.
In the first case, any comparison with NULL returns NULL (even comparisons between NULL values such as yours).
In the second case, sql server will evaluate comparisons between NULL values (e.g. NULL=NULL will return true).
So before considering the different results in your queries you must first consider that comparing NULL with anything, doesn't evaluate to false but NULL