NOT (a LIKE 'foo%')
NOT ( (a,b) OVERLAPS (x,y) )
NOT (a BETWEEN x AND y)
NOT (a IS NULL)
Except for the 
overlaps operator above could also be written as:a NOT LIKE 'foo%'
a NOT BETWEEN x AND y
a IS NOT NULL
In some situations it might be easier to understand to negate a complete expression rather then rewriting it to mean the opposite.
NOT can however be used with <> - but that wouldn't make much sense though: NOT (a <> b) is the same as a = b. Similarly you could use NOT to negate the equality operator NOT (a = b) is the same as a <>b 
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