how to calculate the negation of a selection predicate of a SQL query? - mysql

Question

I have a sql query 'q' which is of the form :
Select attribute from table1, table2 where SC;
Here 'SC' is the conjunction of all the selection predicates in q
In my case : SC is balance <1000 and salary >=50000
Now i want to calculate "NSC" which is negation of SC in q and need some help.

Answer 1

Per your post you said i want to calculate "NSC" which is negation of SC and
SC is balance <1000 and salary >=50000
So, Negation of SC would simply be balance >= 1000 and salary < 50000
So, you can do like
Select attribute from table1 where balance >= 1000 and salary < 50000
(OR)
Select attribute from table1
where attribute not in
( select attribute from table1
where balance <1000 and salary >=50000 )

Answer 2

The general answer to your question is given by De Morgan's laws.
NOT(P AND Q) = NOT(P) OR NOT(Q)
and
NOT(P OR Q) = NOT(P) AND NOT(Q)
Your expression NOT(balance < 1000 AND salary >= 50000) becomes
balance >= 1000 OR salary < 50000
De Morgan's laws apply to Boolean algebra with a binary logic. If you have NULL values, things get more complicated. The way to go depends on the result you are expecting. A very useful function, in this respect, is the COALESCE function which returns the first non-null parameter passed to it.
COALESCE(balance, 0) >= 1000 OR COALESCE(salary, 0) < 50000

Answer 3

Take your pick of two methods.
Aside: null
I will assume there are no NULLs in tables or expressions. Because that complicates things. In particular, if we want to treat NULL as if it were a value in conditions then:
v = w is true in SQL when v = w AND v IS NOT NULL AND w IS NOT NULL
v != w is true in SQL when v != w AND v IS NOT NULL AND
Also SQL has lots of special behaviour when there are nulls. Also beware that nulls get generated by SQL in things like OUTER JOIN and IN of a subquery. See SQL and Relational Theory: How to Write Accurate SQL Code, 2nd Edition.
1. not ( expression )
SQL doesn't have a comparson-negating "not". You can build an expression that is the not of another expression by parsing from the top down:
not (c AND d) is (not (c) OR not (d))
not (c OR d) is (not (c) AND not(d))
not (e NOT NOTable-operator o) is (e NOTable-operator o)
not (e NOTable-operator o) is (e NOT NOTable-operator o)
not (e NOT NOTable-function(f)) is (e NOTable-function(f))
not (e notable-function(f)) is (e NOT NOTable-function(f))
not (e != f) is (e = f)
not (e = f) is (e != f)
not (v < w) is is (v >= w)
not NOT b is b -- boolean b
not b is (NOT (b)) -- boolean b
Now given SC you find expression not(SC) and you write:
SELECT ... FROM ... WHERE not(SC)
2. Not not ( expression )
In standard SQL you could write the preceding query as:
(SELECT ... FROM ...)
EXCEPT
(SELECT ... FROM ... WHERE SC)
(In Oracle it's MINUS.) But MySql doesn't have EXCEPT. But s EXCEPT t is
SELECT s.a,...
FROM s
LEFT JOIN t
ON s.a = t.a AND ...
WHERE t.a IS NULL
When s.a has no match in t, t.a IS NULL. So this returns only unmatched rows. So
SELECT ... FROM ... WHERE not(SC)
is:
SELECT s.a,...
FROM (SELECT ... FROM ...) s
LEFT JOIN (SELECT ... FROM ... WHERE SC) t
ON s.a = t.a AND ...
WHERE t.a IS NULL