Logic Hazard On Equality to Null To Be Considered
The equality operator generates an unknown value when there is a null
and the unknown value is treated a false.
Not (unknown) is still unknown.
In the example below I'll ask if a couple (a1, b1) is equal to (a2, b2).
Note that each column has 3 values: 0, 1 and NULL.
DECLARE @t table (a1 bit, a2 bit, b1 bit, b2 bit)
Insert into @t (a1 , a2, b1, b2) 
values( 0 , 0 , 0 , NULL )
select 
a1,a2,b1,b2,
case when (
    (a1=a2 or (a1 is null and a2 is null))
and (b1=b2 or (b1 is null and b2 is null))
)
then 
'Equal'
end,
case when not (
    (a1=a2 or (a1 is null and a2 is null))
and (b1=b2 or (b1 is null and b2 is null))
)
then 
'Not Equal'
end,
case when (
    (a1<>a2 or (a1 is null and a2 is not null) or (a1 is not null and a2 is null))
or (b1<>b2 or (b1 is null and b2 is not null) or (b1 is not null and b2 is null))
)
then 
'Different'
end
from @t
Note that here, the results we expect are:
- Equal to be null
- Not equal to be not
equal
- Different to be different
But instead, we get another result
- Equal is null - what we expected.
- Not Equal is null  ???
- Different is different - what we expected.