> > Wow.. that is easy except that I do not understand your notice
> > explanation... the difference between your not( ... ) and your !=.
> 
> "@cat != 'BLUE'": will be true if the context node has a 
> 'cat' attribute  
> *and* if it has a 'cat' attribute not equal to 'BLUE'. So 
> it's the same as  
> "boolean(@cat) and not(@cat='BLUE')"
> 
> "not(@cat='BLUE')": will be true if the context node has no 'cat'  
> attribute *or* if it has a 'cat' attribute not equal to 
> 'BLUE'. So it's  
> equal to "not(@cat) or not(@cat='BLUE')"

Let's try to phrase it a different way. An expression such as X=Y in XPath
is shorthand for

some $x in X, $y in Y satisfies $x=$y

in other words, it's true if there's some pair of values from the two sets
that are equal. 

Similarly, X!=Y is short for

some $x in X, $y in Y satisfies $x!=$y

which is true if there's some pair that are not equal.

This means that if X is an empty set, then X=3 and X!=3 must both be false.
If you're testing an attribute, @A=3, then @A is a set that's either empty
or contains one node. If there's no A attribute, then @A!=3 is false
(because there's no A that's not equal to 3), but not(@A=3) is true (because
it's not true that there's an A that's equal to 3).

Michael Kay
http://www.saxonica.com/